A015287 Gaussian binomial coefficient [ n,4 ] for q = -2.

1, 11, 231, 3311, 56287, 875007, 14208447, 225683007, 3624203583, 57881286463, 926949282623, 14824402656063, 237244744338239, 3795481554332479, 60731179948567359, 971671079497526079, 15546959673214593855

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..800

Index entries for linear recurrences with constant coefficients, signature (11,110,-440,-704,1024).

Index entries related to Gaussian binomial coefficients.

Formula

G.f.: x^4/((1-x)*(1+2*x)*(1-4*x)*(1+8*x)*(1-16*x)). - Bruno Berselli, Oct 30 2012

a(n) = (1 - 2^(2n-5)*(15-2^(2n-1)) - (-1)^n*5*2^(n-3)*(1-2^(2n-3)))/1215. - Bruno Berselli, Oct 30 2012

A015287(n) = T[n,4], where T is the triangular array A015109. - M. F. Hasler, Nov 04 2012

Mathematica

Table[QBinomial[n, 4, -2], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Prog

(Sage) [gaussian_binomial(n, 4, -2) for n in range(4, 21)] # Zerinvary Lajos, May 27 2009
(Magma) r:=4; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016

Crossrefs

Diagonal k=4 in the triangular array A015109. See there for further references and programs. - M. F. Hasler, Nov 04 2012

Sequence in context: A346423 A077736 A068122 * A254782 A169960 A045757

Adjacent sequences: A015284 A015285 A015286 * A015288 A015289 A015290

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved