A015433 Gaussian binomial coefficient [ n,12 ] for q=-10.

1, 909090909091, 918273645546455463728191, 917356289257199182819017528926537191, 917448034060605151598548458052424151513398447191, 917438859672008440688621912439351273986143166283578679347191, 917439777111785551556734609501952335249856503700731106092153925870347191

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_{i=1..12} ((-10)^(n-i+1)-1)/((-10)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 12, -10], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

(Sage) [gaussian_binomial(n, 12, -10) for n in range(12, 17)] # Zerinvary Lajos, May 28 2009
(Magma) r:=12; q:=-10; [&*[(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: A297354 A172798 A186017 * A234195 A297356 A172853

Adjacent sequences: A015430 A015431 A015432 * A015434 A015435 A015436

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved