A015365 Gaussian binomial coefficient [ n,8 ] for q=-9.

1, 38742049, 1688564650965445, 72587599955185580267365, 3125134483161392104770081009295, 134524513999723596604019036560420619887, 5790850118312580284352508983888376537699322083

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..140

Crossrefs

Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015357, A015359, A015360, A015361, A015363, A015364, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012

Programs

Magma

r:=8; q:=-9; [&*[(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, -9], {n, 8, 15}] (* Vincenzo Librandi, Nov 03 2012 *)

PARI

A015365(n, r=8, q=-9)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

Sage

[gaussian_binomial(n,8,-9) for n in range(8,14)] # Zerinvary Lajos, May 25 2009

Formula

a(n) = Product_{i=1..8} ((-9)^(n-i+1)-1)/((-9)^i-1). - M. F. Hasler, Nov 03 2012