A015434 Gaussian binomial coefficient [ n,12 ] for q=-11.

1, 2876892678661, 9104162632986302495960347, 28551311330859170052594978984538703567, 89612366318560505321323986969057938917191132920348, 281240247078624326614268823428029385995576471270476701478391628

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..90

Formula

a(n) = product(((-11)^(n-i+1)-1)/((-11)^i-1), i=1..12) (by definition). - Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 12, -11], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

(Sage) [gaussian_binomial(n, 12, -11) for n in range(12, 17)] # Zerinvary Lajos, May 28 2009
(Magma) r:=12; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012

Crossrefs

Sequence in context: A233496 A233617 A323052 * A017292 A017400 A017664

Adjacent sequences: A015431 A015432 A015433 * A015435 A015436 A015437

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved