A015399 Gaussian binomial coefficient [ n,10 ] for q=-11.

1, 23775972551, 621826557818118395106, 16116470915170412804822871108406, 418048302457998082359053173653182700919721, 10843028997901257369999365975865569183708813670389271

Offset

10,2

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 = 10..100

Formula

a(n) = Product_{i=1..10} ((-11)^(n-i+1)-1)/((-11)^i-1) (by definition). - Vincenzo Librandi, Nov 05 2012

Mathematica

Table[QBinomial[n, 10, -11], {n, 10, 20}] (* Vincenzo Librandi, Nov 05 2012 *)

Prog

(Sage) [gaussian_binomial(n, 10, -11) for n in range(10, 16)] # Zerinvary Lajos, May 25 2009
(Magma) r:=10; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 05 2012

Crossrefs

Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015388, A015390, A015391, A015392, A015393, A015394, A015397, A015398, A015401, A015402.

Sequence in context: A368034 A233841 A338374 * A129475 A172612 A293624

Adjacent sequences: A015396 A015397 A015398 * A015400 A015401 A015402

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved