A015302 Gaussian binomial coefficient [ n,4 ] for q = -12.

1, 19141, 399683221, 8283038077141, 171765360605672917, 3561712204486990461397, 73855689005170238163929557, 1531471524472711661173885667797, 31756593605318274408653251348629973

Offset: 4

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 = 4..200
• Index entries for linear recurrences with constant coefficients, signature (19141,33305340,-4795968960,-57154719744,61917364224).

Programs

Mathematica

Table[QBinomial[n, 4, -12], {n, 4, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,4,-12) for n in range(4,13)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: -x^4 / ( (x-1)*(1728*x+1)*(20736*x-1)*(12*x+1)*(144*x-1) ). - R. J. Mathar, Aug 03 2016