|
| |
|
|
A015365
|
|
Gaussian binomial coefficient [ n,8 ] for q=-9.
|
|
13
|
|
|
|
1, 38742049, 1688564650965445, 72587599955185580267365, 3125134483161392104770081009295, 134524513999723596604019036560420619887, 5790850118312580284352508983888376537699322083
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
8,2
|
|
|
REFERENCES
|
J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p, 99.
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 8..140
|
|
|
FORMULA
|
a(n)=product_{i=1..8} ((-9)^(n-i+1)-1)/((-9)^i-1). - M. F. Hasler, Nov 03 2012
|
|
|
MATHEMATICA
|
Table[QBinomial[n, 8, -9], {n, 8, 15}] (* Vincenzo Librandi, Nov 03 2012 *)
|
|
|
PROG
|
(Sage) [gaussian_binomial(n, 8, -9) for n in xrange(8, 14)] # [From Zerinvary Lajos, May 25 2009]
(MAGMA) r:=8; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012
(PARI) A015365(n, r=8, q=-9)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ - M. F. Hasler, Nov 03 2012
|
|
|
CROSSREFS
|
Cf. Gaussian binomial coefficients [n,8] for q=-2,...,-13: A015356, A015357, A015359, A015360, A015361, A015363, A015364, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012
Sequence in context: A206196 A246232 A248710 * A105004 A216006 A233754
Adjacent sequences: A015362 A015363 A015364 * A015366 A015367 A015368
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Olivier Gérard
|
|
|
STATUS
|
approved
|
| |
|
|
