A015384 Gaussian binomial coefficient [ n,9 ] for q=-12.

1, -4762874171, 24747240402737283733, -127616472670861852065241422635, 658504724872263265466971967899949697493, -3397726086395967282512946130260694347212577518123

Offset

9,2

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 = 9..110

Formula

a(n) = Product_{i=1..9} ((-12)^(n-i+1)-1)/((-12)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012

Mathematica

Table[QBinomial[n, 9, -12], {n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Prog

(Magma) r:=9; q:=-12; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012

Crossrefs

Cf. Gaussian binomial coefficients [n, 9] for q = -2..-13: A015371, A015375, A015376, A015377, A015378, A015379, A015380, A015381, A015382, A015383, A015385.

Sequence in context: A233494 A175568 A224472 * A233615 A217146 A072018

Adjacent sequences: A015381 A015382 A015383 * A015385 A015386 A015387

Keyword

sign,easy

Author

Olivier Gérard

Status

approved