A015323 Gaussian binomial coefficient [ n,6 ] for q = -2.

1, 43, 3655, 208335, 14208447, 882215391, 57344000415, 3642010817055, 233988483199263, 14946527496991519, 957498220445101855, 61250446192484546335, 3920970870875818419999, 250911985465716094666527

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 (43,1806,-26488,-211904,924672,1409024,-2097152).

Crossrefs

Diagonal k=6 of the triangular array A015109. See there for further references and programs. - M. F. Hasler, Nov 04 2012

Programs

Mathematica

Table[QBinomial[n, 6, -2], {n, 6, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,6,-2) for n in range(6,20)] # Zerinvary Lajos, May 27 2009

Formula

A015323(n) = T[n,6] where T is the triangular array A015109. - M. F. Hasler, Nov 04 2012

G.f.: x^6 / ( (x-1)*(8*x+1)*(64*x-1)*(2*x+1)*(32*x+1)*(4*x-1)*(16*x-1) ). - R. J. Mathar, Aug 04 2016