A015401 Gaussian binomial coefficient [ n,10 ] for q=-12.

1, 57154490053, 3563602618051323347605, 220521264778812882986788501660885, 13654753975171772337501943609360145428875733, 845462977543736084817433183822531039414960234418458069

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} ((-12)^(n-i+1)-1)/((-12)^i-1) (by definition). - Vincenzo Librandi, Nov 05 2012

Mathematica

Table[QBinomial[n, 10, -12], {n, 10, 20}] (* Vincenzo Librandi, Nov 05 2012 *)

Prog

(Sage) [gaussian_binomial(n, 10, -12) for n in range(10, 15)] # Zerinvary Lajos, May 25 2009
(Magma) r:=10; q:=-12; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012

Crossrefs

Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015388, A015390, A015391, A015392, A015393, A015394, A015397, A015398, A015399, A015402.

Sequence in context: A346365 A295042 A320880 * A273930 A273931 A273933

Adjacent sequences: A015398 A015399 A015400 * A015402 A015403 A015404

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved