A015429 Gaussian binomial coefficient [ n,12 ] for q=-6.

1, 1865813431, 4177511710786827427, 9051628015237517688012698587, 19718638974813744289323111717093729163, 42917665763197914342331213431251480044434903403

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..120

Formula

a(n) = Product_{i=1..12} ((-6)^(n-i+1)-1)/((-6)^i-1). - Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 12, -6], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

(Sage) [gaussian_binomial(n, 12, -6) for n in range(12, 18)] # Zerinvary Lajos, May 28 2009
(Magma) r:=12; q:=-6; [&*[(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: A251401 A325900 A251282 * A263562 A204813 A103752

Adjacent sequences: A015426 A015427 A015428 * A015430 A015431 A015432

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved