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

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

Offset

12,2

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A330678 A250831 A184772 * A352329 A353025 A345609

Adjacent sequences: A015422 A015423 A015424 * A015426 A015427 A015428

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved