A015432 Gaussian binomial coefficient [ n,12 ] for q=-9.

1, 254186582833, 72687171253825493271271, 20500882161928535478431441379312055, 5790937276726544621284284010937628428554805020, 1635504033452004972838895174119166771419593874338342173788, 461915515256190228639422934162753182948200513062452706826160310202324

Offset

12,2

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 = 12..100

Formula

a(n) = Product_{i=1..12} ((-9)^(n-i+1)-1)/((-9)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 12, -9], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

(Sage) [gaussian_binomial(n, 12, -9) for n in range(12, 17)] # Zerinvary Lajos, May 28 2009
(Magma)  r:=12; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012

Crossrefs

Sequence in context: A076254 A213689 A348800 * A034618 A226858 A216904

Adjacent sequences: A015429 A015430 A015431 * A015433 A015434 A015435

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved