A015430 Gaussian binomial coefficient [ n,12 ] for q=-7.

1, 12111126301, 171125943656551078651, 2361717858885719498568905414551, 32702835678888952715367233418017870232604, 452622410329553863939387656214689217248493781677804

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..110

Formula

a(n) = Product_{i=1..12} ((-7)^(n-i+1)-1)/((-7)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 12, -7], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

(Sage) [gaussian_binomial(n, 12, -7) for n in range(12, 18)] # Zerinvary Lajos, May 28 2009
(Magma) r:=12; q:=-7; [&*[(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: A213534 A366897 A202361 * A135496 A287747 A113642

Adjacent sequences: A015427 A015428 A015429 * A015431 A015432 A015433

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved