A015363 Gaussian binomial coefficient [ n,8 ] for q=-7.

1, 5044201, 29684623509101, 170628488227082949701, 984049129188697468764456303, 5672509895284807570626050787828903, 32701168672146988445875611556849499108603, 188515500954498588979354521825234382842445990403

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, A015364, A015365, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012

Programs

Magma

r:=8; q:=-7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012

Mathematica

QBinomial[Range[8,20],8,-7] (* Harvey P. Dale, May 09 2012 *)
Table[QBinomial[n, 8, -7], {n, 8, 19}] (* Vincenzo Librandi, Nov 03 2012 *)

PARI

A015363(n, r=8, q=-7)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

Sage

[gaussian_binomial(n,8,-7) for n in range(8,15)] # Zerinvary Lajos, May 25 2009

Formula

a(n) = Product_{i=1..8} ((-7)^(n-i+1)-1)/((-7)^i-1). - M. F. Hasler, Nov 03 2012