A015431 Gaussian binomial coefficient [ n,12 ] for q=-8.

1, 61083979321, 4264288605349394427001, 292468454161371994489927453227641, 20103187136428193301141459556344509715532409, 1381438342588687480407961010312719764427906885156653689, 94932082182896025238148883982319050364413593497347296287825382009

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} ((-8)^(n-i+1)-1)/((-8)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 12, -8], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

(Sage) [gaussian_binomial(n, 12, -8) for n in range(12, 17)] # Zerinvary Lajos, May 28 2009
(Magma) r:=12; q:=-8; [&*[(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: A273933 A196753 A258424 * A273934 A017410 A017530

Adjacent sequences: A015428 A015429 A015430 * A015432 A015433 A015434

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved