Search: keyword:new
|
| |
|
|
A271770
|
|
Number of set partitions of [n] with minimal block length multiplicity equal to ten.
|
|
+0
0
|
|
|
|
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 654729075, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1228555090548911125, 55437426478058625, 1034831960923761000, 375268733082243000, 42378561928787584500, 2126522820799377000, 2014348742002209863250, 10413707343032243250
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
10,11
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 10..578
Wikipedia, Partition of a set
|
|
|
FORMULA
|
a(n) = A271424(n,10).
|
|
|
MAPLE
|
with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
*b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
end:
a:= n-> b(n$2, 10)-b(n$2, 11):
seq(a(n), n=10..40);
|
|
|
CROSSREFS
|
Column k=10 of A271424.
|
|
|
KEYWORD
|
nonn,new
|
|
|
AUTHOR
|
Alois P. Heinz, Apr 13 2016
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A271769
|
|
Number of set partitions of [n] with minimal block length multiplicity equal to nine.
|
|
+0
0
|
|
|
|
1, 0, 0, 0, 0, 0, 0, 0, 0, 34459425, 0, 0, 0, 0, 0, 0, 0, 0, 3139051466175625, 452214824811750, 7749317679728625, 2980506799895625, 284294494759275000, 16245399700530000, 12231973704514063500, 75947243599977750, 558368602431954063750, 668351312267239068593125
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
9,10
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 9..578
Wikipedia, Partition of a set
|
|
|
FORMULA
|
a(n) = A271424(n,9).
|
|
|
MAPLE
|
with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
*b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
end:
a:= n-> b(n$2, 9)-b(n$2, 10):
seq(a(n), n=9..40);
|
|
|
CROSSREFS
|
Column k=9 of A271424.
|
|
|
KEYWORD
|
nonn,new
|
|
|
AUTHOR
|
Alois P. Heinz, Apr 13 2016
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A271768
|
|
Number of set partitions of [n] with minimal block length multiplicity equal to eight.
|
|
+0
0
|
|
|
|
1, 0, 0, 0, 0, 0, 0, 0, 2027025, 0, 0, 0, 0, 0, 0, 0, 10652498631775, 4141161399375, 64602117830250, 26428139112375, 2096632369581750, 137561852302875, 80768458994973750, 609202488769875, 158980016052580597875, 353341814230502847750, 1344898884799733513250
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
8,9
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 8..578
Wikipedia, Partition of a set
|
|
|
FORMULA
|
a(n) = A271424(n,8).
|
|
|
MAPLE
|
with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
*b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
end:
a:= n-> b(n$2, 8)-b(n$2, 9):
seq(a(n), n=8..35);
|
|
|
CROSSREFS
|
Column k=8 of A271424.
|
|
|
KEYWORD
|
nonn,new
|
|
|
AUTHOR
|
Alois P. Heinz, Apr 13 2016
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A271767
|
|
Number of set partitions of [n] with minimal block length multiplicity equal to seven.
|
|
+0
0
|
|
|
|
1, 0, 0, 0, 0, 0, 0, 135135, 0, 0, 0, 0, 0, 0, 51925673800, 43212118950, 607370338575, 265034329560, 17166996346500, 1305093289500, 584129638842750, 56071685084790375, 176898040019801100, 518112685551586125, 26529011711988035250, 4672320885518286000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
7,8
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 7..577
Wikipedia, Partition of a set
|
|
|
FORMULA
|
a(n) = A271424(n,7):
|
|
|
MAPLE
|
with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
*b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
end:
a:= n-> b(n$2, 7)-b(n$2, 8):
seq(a(n), n=7..35);
|
|
|
CROSSREFS
|
Column k=7 of A271424.
|
|
|
KEYWORD
|
nonn,new
|
|
|
AUTHOR
|
Alois P. Heinz, Apr 13 2016
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A271766
|
|
Number of set partitions of [n] with minimal block length multiplicity equal to six.
|
|
+0
0
|
|
|
|
1, 0, 0, 0, 0, 0, 10395, 0, 0, 0, 0, 0, 383563180, 523783260, 6547290750, 3055402350, 157964301495, 14054850810, 34828180582195, 91670862398500, 448593283888750, 11612610774464700, 7681370284312725, 6594450798260325, 179804372693675480751, 11896760875264765500
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
6,7
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 6..577
Wikipedia, Partition of a set
|
|
|
FORMULA
|
a(n) = A271424(n,6).
|
|
|
MAPLE
|
with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
*b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
end:
a:= n-> b(n$2, 6)-b(n$2, 7):
seq(a(n), n=6..30);
|
|
|
CROSSREFS
|
Column k=6 of A271424.
|
|
|
KEYWORD
|
nonn,new
|
|
|
AUTHOR
|
Alois P. Heinz, Apr 13 2016
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A271765
|
|
Number of set partitions of [n] with minimal block length multiplicity equal to five.
|
|
+0
0
|
|
|
|
1, 0, 0, 0, 0, 945, 0, 0, 0, 0, 4239235, 7567560, 82702620, 41351310, 1658646990, 24448068645, 117626817945, 239611442070, 8260908743395, 1834189492520, 4508736346382576, 2979073800027325, 256635727575051825, 2371542394294648575, 16374593589666387075
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
5,6
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 5..577
Wikipedia, Partition of a set
|
|
|
FORMULA
|
a(n) = A271424(n,5).
|
|
|
MAPLE
|
with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
*b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
end:
a:= n-> b(n$2, 5)-b(n$2, 6):
seq(a(n), n=5..30);
|
|
|
CROSSREFS
|
Column k=5 of A271424.
|
|
|
KEYWORD
|
nonn,new
|
|
|
AUTHOR
|
Alois P. Heinz, Apr 13 2016
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A271764
|
|
Number of set partitions of [n] with minimal block length multiplicity equal to four.
|
|
+0
0
|
|
|
|
1, 0, 0, 0, 105, 0, 0, 0, 67375, 135135, 1261260, 675675, 50925875, 97847750, 703993290, 6215737710, 228687298476, 58017429575, 11262925616250, 72813288304295, 2841531210935725, 11311740884766630, 252469888906590355, 2207276997956560530, 28579415631325499655
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
4,5
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 4..577
Wikipedia, Partition of a set
|
|
|
FORMULA
|
a(n) = A271424(n,4).
|
|
|
MAPLE
|
with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
*b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
end:
a:= n-> b(n$2, 4)-b(n$2, 5):
seq(a(n), n=4..30);
|
|
|
CROSSREFS
|
Column k=4 of A271424.
|
|
|
KEYWORD
|
nonn,new
|
|
|
AUTHOR
|
Alois P. Heinz, Apr 13 2016
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A271489
|
|
Maximal terms of TRIP-Stern sequence corresponding to permutation triple (e,132,e).
|
|
+0
0
|
|
|
|
1, 2, 3, 4, 5, 7, 10, 13, 18, 25, 34
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
I. Amburg, K. Dasaratha, L. Flapan, T. Garrity, C. Lee, C. Mihailak, N. Neumann-Chun, S. Peluse, M. Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239v1 [math.CO] 17 Sep 2015. See Conecture 5.8.
|
|
|
LINKS
|
Table of n, a(n) for n=0..10.
|
|
|
CROSSREFS
|
For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.
|
|
|
KEYWORD
|
nonn,more,new
|
|
|
AUTHOR
|
N. J. A. Sloane, Apr 13 2016
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A271488
|
|
Maximal terms of TRIP-Stern sequence corresponding to permutation triple (e,23,e).
|
|
+0
0
|
|
|
|
1, 2, 3, 4, 6, 8, 11, 15, 21, 30, 41
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
I. Amburg, K. Dasaratha, L. Flapan, T. Garrity, C. Lee, C. Mihailak, N. Neumann-Chun, S. Peluse, M. Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239v1 [math.CO] 17 Sep 2015. See Conecture 5.8.
|
|
|
LINKS
|
Table of n, a(n) for n=0..10.
|
|
|
CROSSREFS
|
For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.
|
|
|
KEYWORD
|
nonn,more,new
|
|
|
AUTHOR
|
N. J. A. Sloane, Apr 13 2016
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A271487
|
|
Maximal terms of TRIP-Stern sequence corresponding to permutation triple (e,13,132).
|
|
+0
0
|
|
|
|
1, 2, 3, 4, 6, 8, 11, 17, 23, 32, 48
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
I. Amburg, K. Dasaratha, L. Flapan, T. Garrity, C. Lee, C. Mihailak, N. Neumann-Chun, S. Peluse, M. Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239v1 [math.CO] 17 Sep 2015. See Conecture 5.8.
|
|
|
LINKS
|
Table of n, a(n) for n=0..10.
|
|
|
CROSSREFS
|
For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.
|
|
|
KEYWORD
|
nonn,more,new
|
|
|
AUTHOR
|
N. J. A. Sloane, Apr 13 2016
|
|
|
STATUS
|
approved
|
| |
|
Search completed in 0.216 seconds
|
