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

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

Offset

8,2

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

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

Mathematica

Table[QBinomial[n, 8, -5], {n, 8, 20}] (* Vincenzo Librandi, Nov 03 2012 *)

Prog

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

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

Sequence in context: A186836 A237223 A250910 * A209847 A237306 A210387

Adjacent sequences: A015357 A015358 A015359 * A015361 A015362 A015363

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved