A015409 Gaussian binomial coefficient [ n,11 ] for q=-5.

1, -40690104, 2069605714586046, -100252942972187432169704, 4903008044094795843516454343421, -239328104658006678585444195424892284704, 11686690558465291130135333443500921076518590296, -570631883336806742698184435808699328319904985223284704

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..140

Formula

a(n) = Product_{i=1..11} ((-5)^(n-i+1)-1)/((-5)^i-1) (by definition). - Vincenzo Librandi, Nov 05 2012

Mathematica

Table[QBinomial[n, 11, -5], {n, 11, 20}] (* Vincenzo Librandi, Nov 05 2012 *)

Prog

(SageMath) [gaussian_binomial(n, 11, -5) for n in range(11, 17)] # Zerinvary Lajos, May 28 2009
(Magma) r:=11; q:=-5; [&*[(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: A017361 A017481 A017613 * A178204 A334583 A130681

Adjacent sequences: A015406 A015407 A015408 * A015410 A015411 A015412

Keyword

sign,easy

Author

Olivier Gérard

Status

approved