A015292 Gaussian binomial coefficient [ n,4 ] for q = -6.

1, 1111, 1480963, 1910490043, 2477905585771, 3210953026617931, 4161484248724884235, 5393264335151280477835, 6989674736616919292088715, 9058617560471271225871839115, 11739968552378570066280405695371

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..300
• Index entries for linear recurrences with constant coefficients, signature (1111, 246642, -8879112, -51834816, 60466176).

Programs

Magma

r:=4; q:=-6; [&*[(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, -6], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Sage

[gaussian_binomial(n,4,-6) for n in range(4,15)] # Zerinvary Lajos, May 27 2009