A015425 Gaussian binomial coefficient [ n,12 ] for q=-4.

1, 13421773, 240191982810781, 3967756584209486471005, 66828959857649638516515454045, 1120110037194182450025632158559979613, 18796917128597217472986991275660647159371869

Offset: 12

Author

Olivier Gérard

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 = 12..150

Programs

Magma

r:=12; q:=-4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 12, -4], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Sage

[gaussian_binomial(n,12,-4) for n in range(12,19)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = Product_{i=1..12} ((-4)^(n-i+1)-1)/((-4)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012