A015417 Gaussian binomial coefficient [ n,11 ] for q=-10.

1, -90909090909, 9182736455455463728191, -917356289256280909173471073462809, 91744803405968779530929125886960513398447191, -9174388596710909926545613072877527255280907421320652809

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..100

Formula

a(n) = Product_{i=1..11} ((-10)^(n-i+1)-1)/((-10)^i-1). - Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 11, -10], {n, 11, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

(Sage) [gaussian_binomial(n, 11, -10) for n in range(11, 16)] # Zerinvary Lajos, May 28 2009
(Magma) r:=11; q:=-10; [&*[(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: A283459 A153433 A234386 * A217468 A234052 A104831

Adjacent sequences: A015414 A015415 A015416 * A015418 A015419 A015420

Keyword

sign,easy

Author

Olivier Gérard

Status

approved