A015360 Gaussian binomial coefficient [ n,8 ] for q=-5.

1, 325521, 132454820421, 51329529054158421, 20082729571968536374671, 7842306707330337276457324671, 3063597127265150338968694860387171, 1196702310087594273181943625299134137171, 467463036580276600555969910576099571466559046

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..190

Crossrefs

Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015357, A015359, A015361, A015363, A015364, A015365, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012

Programs

Magma

r:=8; q:=-5; [&*[(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, -5], {n, 8, 20}] (* Vincenzo Librandi, Nov 03 2012 *)

PARI

A015360(n,r=8,q=-5)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

Sage

[gaussian_binomial(n,8,-5) for n in range(8,16)] # Zerinvary Lajos, May 25 2009

Formula

a(n) = Product_{i=1..8} ((-5)^(n-i+1)-1)/((-5)^i-1). - M. F. Hasler, Nov 03 2012

G.f.: -x^8 / ( (x-1)*(5*x+1)*(390625*x-1)*(25*x-1)*(625*x-1)*(78125*x+1)*(125*x+1)*(15625*x-1)*(3125*x+1) ). - R. J. Mathar, Sep 02 2016