A015432 Gaussian binomial coefficient [ n,12 ] for q=-9.

1, 254186582833, 72687171253825493271271, 20500882161928535478431441379312055, 5790937276726544621284284010937628428554805020, 1635504033452004972838895174119166771419593874338342173788, 461915515256190228639422934162753182948200513062452706826160310202324

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..100

Programs

Magma

r:=12; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 12, -9], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Sage

[gaussian_binomial(n,12,-9) for n in range(12,17)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = Product_{i=1..12} ((-9)^(n-i+1)-1)/((-9)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012