A015377 Gaussian binomial coefficient [ n,9 ] for q=-5.

1, -1627604, 3311368882921, -6416187820400919704, 12551699566292514833249671, -24507195908707737696414306347204, 47868680606322065338648160779243199671, -93492320106912696270274007078334075223284704

Offset

9,2

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 = 9..170

Formula

a(n) = Product_{i=1..9} ((-5)^(n-i+1)-1)/((-5)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012

Mathematica

Table[QBinomial[n, 9, -5], {n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Prog

(Sage) [gaussian_binomial(n, 9, -5) for n in range(9, 16)] # Zerinvary Lajos, May 25 2009]
(Magma) r:=9; q:=-5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012

Crossrefs

Cf. Gaussian binomial coefficients [n,9] for q=-2..-13: A015371, A015375, A015376, A015378, A015379, A015380, A015381, A015382, A015383, A015384, A015385. - Vincenzo Librandi, Nov 04 2012

Sequence in context: A064117 A173428 A015334 * A296450 A255042 A255035

Adjacent sequences: A015374 A015375 A015376 * A015378 A015379 A015380

Keyword

sign,easy

Author

Olivier Gérard

Status

approved