A015414 Gaussian binomial coefficient [ n,11 ] for q=-9.

1, -28242953648, 897372484611991440598, -28121923404466184234811544425296, 882630281467161063728449241801432249226565, -27697404417453539188846019907159858548132165589760832, 869175534545800426775448129124238227336771807766117241522242296

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} ((-9)^(n-i+1)-1)/((-9)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 11, -9], {n, 11, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

(Sage) [gaussian_binomial(n, 11, -9) for n in range(11, 17)] # Zerinvary Lajos, May 28 2009
(Magma) r:=11; q:=-9; [&*[(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: A017662 A120322 A324977 * A252839 A307760 A216017

Adjacent sequences: A015411 A015412 A015413 * A015415 A015416 A015417

Keyword

sign,easy

Author

Olivier Gérard

Status

approved