A015410 Gaussian binomial coefficient [ n,11 ] for q=-6.

1, -310968905, 116041991914472611, -41905685236388916561230885, 15214999201976941569510489219969931, -5519247137793116688209551072778853951561365, 2002409531513525089470147425061900304433199288073771

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..120

Formula

a(n) = Product_{i=1..11} ((-6)^(n-i+1)-1)/((-6)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 11, -6], {n, 11, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

(Sage) [gaussian_binomial(n, 11, -6) for n in range(11, 17)] # Zerinvary Lajos, May 28 2009
(Magma) r:=11; q:=-6; [&*[(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: A251807 A184671 A034610 * A189055 A221985 A219784

Adjacent sequences: A015407 A015408 A015409 * A015411 A015412 A015413

Keyword

sign,easy

Author

Olivier Gérard

Status

approved