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

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..800
• Index entries for linear recurrences with constant coefficients, signature (11,110,-440,-704,1024).
• Index entries related to Gaussian binomial coefficients.

Crossrefs

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

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,4,-2) for n in range(4,21)] # Zerinvary Lajos, May 27 2009

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