A015391 Gaussian binomial coefficient [ n,10 ] for q=-5.

1, 8138021, 82784230211046, 802023560334345174046, 7844813030956382105126218421, 76584995059524711257676812461230921, 747948211058777330441088769852487456090296, 7304088256300765454892487244083619479306573590296

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..150

Crossrefs

Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015388, A015390, A015392, A015393, A015394, A015397, A015398, A015399, A015401, A015402.

Programs

Magma

r:=10; q:=-5; [&*[(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, -5], {n, 10, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Sage

[gaussian_binomial(n,10,-5) for n in range(10,17)] # Zerinvary Lajos, May 25 2009

Formula

a(n) = Product_{i=1..10} ((-5)^(n-i+1)-1)/((-5)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012