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

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

Offset

4,2

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 = 4..200

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

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A237554 A263024 A367650 * A249106 A184196 A210316

Adjacent sequences: A015299 A015300 A015301 * A015303 A015304 A015305

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved