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

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

Offset: 9

Author

Olivier Gérard

Keywords

• sign
• 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 = 9..170

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

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,9,-5) for n in range(9,16)] # Zerinvary Lajos, May 25 2009

Formula

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