A015369 Gaussian binomial coefficient [ n,8 ] for q=-12.

1, 396906181, 171855836163195541, 73852125402551558141191381, 31756593605318274408653251348629973, 13654699102424414895934644240803700147539413, 5871272644707452307243912611380074655778555267227093

Offset: 8

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 = 8..100

Crossrefs

Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015357, A015359, A015360, A015361, A015363, A015364, A015365, A015367, A015368, A015370. - M. F. Hasler, Nov 03 2012

Programs

Magma

r:=8; q:=-12; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012

Maple

A015369:=n->mul(((-12)^(n-i+1)-1)/((-12)^i-1), i=1..8): seq(A015369(n), n=8..20); # Wesley Ivan Hurt, Jan 29 2017

Mathematica

Table[QBinomial[n, 8, -12], {n, 8, 14}] (* Vincenzo Librandi, Nov 03 2012 *)

PARI

A015369(n,r=8,q=-12)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

Sage

[gaussian_binomial(n,8,-12) for n in range(8,14)] # Zerinvary Lajos, May 24 2009

Formula

a(n) = Product_{i=1..8} ((-12)^(n-i+1)-1)/((-12)^i-1). - M. F. Hasler, Nov 03 2012