|
| |
|
|
A304964
|
|
Expansion of 1/(1 - Sum_{i>=1, j>=1, k>=1, l>=1} x^(i*j*k*l)).
|
|
2
|
|
|
|
1, 1, 5, 13, 47, 133, 443, 1333, 4263, 13143, 41419, 128791, 403815, 1259639, 3941579, 12310299, 38492034, 120271953, 375964616, 1174935195, 3672413322, 11477465221, 35872928244, 112117013835, 350417746650, 1095202995267, 3422999582632, 10698350241417, 33437065631262, 104505382585023
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Invert transform of A007426.
|
|
|
LINKS
|
Table of n, a(n) for n=0..29.
N. J. A. Sloane, Transforms
Index entries for sequences related to compositions
|
|
|
FORMULA
|
G.f.: 1/(1 - Sum_{k>=1} A007426(k)*x^k).
|
|
|
MAPLE
|
A:= proc(n, k) option remember; `if`(k=1, 1,
add(A(d, k-1), d=numtheory[divisors](n)))
end:
a:= proc(n) option remember; `if`(n=0, 1,
add(A(j, 4)*a(n-j), j=1..n))
end:
seq(a(n), n=0..35); # Alois P. Heinz, May 22 2018
|
|
|
MATHEMATICA
|
nmax = 29; CoefficientList[Series[1/(1 - Sum[x^(i j k l), {i, 1, nmax}, {j, 1, nmax/i}, {k, 1, nmax/i/j}, {l, 1, nmax/i/j/k}]), {x, 0, nmax}], x]
nmax = 29; CoefficientList[Series[1/(1 - Sum[Sum[DivisorSigma[0, d] DivisorSigma[0, k/d], {d, Divisors[k]}] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Sum[DivisorSigma[0, d] DivisorSigma[0, k/d], {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 29}]
|
|
|
CROSSREFS
|
Cf. A000005, A007426, A011782, A129921, A280486, A280487, A304963.
Sequence in context: A217892 A194639 A152925 * A120790 A162563 A250133
Adjacent sequences: A304961 A304962 A304963 * A304965 A304966 A304967
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Ilya Gutkovskiy, May 22 2018
|
|
|
STATUS
|
approved
|
| |
|
|
