A015361 Gaussian binomial coefficient [ n,8 ] for q=-6.

1, 1439671, 2487182817955, 4158260859792814555, 6989674736616919292088715, 11738459947705882553575280369515, 19716527736890127515275338116221320235, 33116077152651051199781730118147946460139435, 55622326158904300663023790195853299389540017396395

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..170

Crossrefs

Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015357, A015359, A015360, A015363, A015364, A015365, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012

Programs

Magma

r:=8; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012

Mathematica

Table[QBinomial[n, 8, -6], {n, 8, 19}] (* Vincenzo Librandi, Nov 03 2012 *)

PARI

A015361(n, r=8, q=-6)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

Sage

[gaussian_binomial(n,8,-6) for n in range(8,15)] # Zerinvary Lajos, May 25 2009

Formula

a(n) = Product_{i=1..8} ((-6)^(n-i+1)-1)/((-6)^i-1). - M. F. Hasler, Nov 03 2012

G.f.: -x^8 / ( (x-1)*(279936*x+1)*(216*x+1)*(36*x-1)*(7776*x+1)*(1296*x-1)*(6*x+1)*(46656*x-1)*(1679616*x-1) ). - R. J. Mathar, Sep 02 2016