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

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

Offset: 10

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 = 10..200

Crossrefs

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

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,10,-3) for n in range(10,18)] # Zerinvary Lajos, May 25 2009

Formula

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