A015272 Gaussian binomial coefficient [ n,3 ] for q = -5.

1, -104, 13546, -1679704, 210302171, -26279294704, 3285123767796, -410635172794704, 51329529054158421, -6416187820400919704, 802023560334345174046, -100252942972187432169704

Offset

3,2

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 = 3..200

Index entries for linear recurrences with constant coefficients, signature (-104,2730,13000,-15625).

Formula

G.f.: x^3/((1-x)*(1+5*x)*(1-25*x)*(1+125*x)). - Bruno Berselli, Oct 29 2012

a(n) = (-1 + 21*5^(2n-3) + (-1)^n*5^(n-2)*(21-5^(2n-1)))/18144. - Bruno Berselli, Oct 29 2012

Mathematica

Table[QBinomial[n, 3, -5], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)
LinearRecurrence[{-104, 2730, 13000, -15625}, {1, -104, 13546, -1679704}, 20] (* Harvey P. Dale, Apr 29 2022 *)

Prog

(Sage) [gaussian_binomial(n, 3, -5) for n in range(3, 15)] # Zerinvary Lajos, May 27 2009

Crossrefs

Sequence in context: A164759 A206013 A187700 * A048920 A091539 A157874

Adjacent sequences: A015269 A015270 A015271 * A015273 A015274 A015275

Keyword

sign,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved