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

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

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..200

Formula

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

Mathematica

Table[QBinomial[n, 12, -2], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

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

Crossrefs

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

Sequence in context: A116461 A266229 A076575 * A260543 A145647 A251946

Adjacent sequences: A015420 A015421 A015422 * A015424 A015425 A015426

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved