A015388 Gaussian binomial coefficient [ n,10 ] for q=-3.

1, 44287, 2941985410, 167517069529030, 10015359787639069513, 588973263031690760850991, 34826053765400471578213696840, 2055503791013087031667210071738520, 121393945396362834176064326157233601646

Offset

10,2

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 = 10..200

Formula

a(n) = Product_{i=1..10} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012

Mathematica

Table[QBinomial[n, 10, -3], {n, 10, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Prog

(Sage) [gaussian_binomial(n, 10, -3) for n in range(10, 18)] # Zerinvary Lajos, May 25 2009
(Magma) r:=10; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 04 2012

Crossrefs

Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015390, A015391, A015392, A015393, A015394, A015397, A015398, A015399, A015401, A015402.

Sequence in context: A193055 A240099 A245483 * A257714 A204668 A115959

Adjacent sequences: A015385 A015386 A015387 * A015389 A015390 A015391

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved