A015324 Gaussian binomial coefficient [ n,6 ] for q = -3.

1, 547, 448540, 315323620, 232740363922, 168973319623174, 123350523324917020, 89881489830655851460, 65533580739687859229563, 47771556642163840723529281, 34826053765400471578213696840

Offset: 6

Author

Olivier Gérard, Dec 11 1999

Keywords

• nonn
• easy

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 = 6..200
• Index entries for linear recurrences with constant coefficients, signature (547,149331,-11711817,-316219059,2939282073,7848852129,-10460353203).

Crossrefs

Gaussian binomial coefficient [n, k]_q for q = -3: A015251 (k = 2), A015268 (k = 3), A015288 (k = 4), A015306 (k = 5), this sequence (k = 6), A015340 (k = 7), A015357 (k = 8), A015375 (k = 9), A015388 (k = 10).

Programs

Mathematica

Table[QBinomial[n, 6, -3], {n, 6, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,6,-3) for n in range(6,17)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^6 / ( (x-1)*(27*x+1)*(81*x-1)*(729*x-1)*(9*x-1)*(3*x+1)*(243*x+1) ). - R. J. Mathar, Aug 04 2016

G.f. with offset 0: exp(Sum_{n >= 1} A015518(7*n)/A015518(n) * (-x)^n/n) = 1 + 547*x + 448540*x^2 + .... - Peter Bala, Jun 29 2025