A015408 Gaussian binomial coefficient [ n,11 ] for q=-4.

1, -3355443, 15011998086813, -61996192875273494691, 261050608944894743386831965, -1093857392934787687867181291059107, 4589090822384565497755014953620236474461, -19246867256860431244800698494652605702283863971

Offset

11,2

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 = 11..150

Formula

a(n) = Product_{i=1..11} ((-4)^(n-i+1)-1)/((-4)^i-1) (by definition). - Vincenzo Librandi, Nov 05 2012

Mathematica

Table[QBinomial[n, 11, -4], {n, 11, 20}] (* Vincenzo Librandi, Nov 05 2012 *)

Prog

(Sage) [gaussian_binomial(n, 11, -4) for n in range(11, 18)] # Zerinvary Lajos, May 28 2009
(Magma)  r:=11; q:=-4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 05 2012

Crossrefs

Sequence in context: A116306 A257917 A257916 * A036472 A206168 A206382

Adjacent sequences: A015405 A015406 A015407 * A015409 A015410 A015411

Keyword

sign,easy

Author

Olivier Gérard

Status

approved