A015407 Gaussian binomial coefficient [ n,11 ] for q=-3.

1, -132860, 26477735830, -4522934399547980, 811239619864365082573, -143119691677080990521708240, 25388050075285266699527263288120, -4495361402895546052989488899628855120

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..200

Formula

a(n) = Product_{i=1..11} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - Vincenzo Librandi, Nov 05 2012

Mathematica

Table[QBinomial[n, 11, -3], {n, 11, 20}] (* Vincenzo Librandi, Nov 05 2012 *)

Prog

(Sage) [gaussian_binomial(n, 11, -3) for n in range(11, 19)] # Zerinvary Lajos, May 28 2009
(Magma) r:=11; q:=-3; [&*[(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: A339535 A319063 A344830 * A204536 A061732 A023046

Adjacent sequences: A015404 A015405 A015406 * A015408 A015409 A015410

Keyword

sign,easy

Author

Olivier Gérard

Status

approved