A015340 Gaussian binomial coefficient [ n,7 ] for q = -3.

1, -1640, 4035220, -8509702520, 18843459775162, -41041673208656120, 89881489830655851460, -196480936769813691291560, 429769342296322230713871283, -939857780045414554730512966640

Offset

7,2

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 = 7..200

Index entries for linear recurrences with constant coefficients, signature (-1640,1345620,314875080,-25929962838,-688631799960,6436058745780,17154979252920,-22876792454961).

Formula

G.f.: x^7 / ( (x-1)*(27*x+1)*(81*x-1)*(729*x-1)*(9*x-1)*(2187*x+1)*(3*x+1)*(243*x+1) ). - R. J. Mathar, Sep 02 2016

G.f. with offset 0: exp(Sum_{n >= 1} A015518(8*n)/A015518(n) * (-x)^n/n) = 1 - 1640*x + 4035220*x^2 - .... - Peter Bala, Jun 29 2025

Mathematica

Table[QBinomial[n, 7, -3], {n, 7, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Prog

(SageMath) [gaussian_binomial(n, 7, -3) for n in range(7, 17)] # Zerinvary Lajos, May 27 2009

Crossrefs

Gaussian binomial coefficient [n, k]_q for q = -3: A015251 (k = 2), A015268 (k = 3), A015288 (k = 4), A015306 (k = 5), A015324 (k = 6), this sequence (k = 7), A015357 (k = 8), A015375 (k = 9), A015388 (k = 10).

Sequence in context: A002434 A146300 A035866 * A272127 A252197 A135016

Adjacent sequences: A015337 A015338 A015339 * A015341 A015342 A015343

Keyword

sign,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved