A015423 Gaussian binomial coefficient [ n,12 ] for q=-2.

1, 2731, 14913991, 54301841231, 237244744338239, 942314556807454559, 3920970870875818419999, 15935828658299317547308959, 65529064844612576067331339935, 267883966717492783113707839256735

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..200

Crossrefs

Diagonal k=12 of the triangular array A015109. See there for further references and programs. - M. F. Hasler, Nov 04 2012

Programs

Magma

r:=12; q:=-2; [&*[(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, -2], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Sage

[gaussian_binomial(n,12,-2) for n in range(12,22)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = Product_{i=1..12} ((-2)^(n-i+1)-1)/((-2)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012