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A015291 Gaussian binomial coefficient [ n,4 ] for q = -5. 2
1, 521, 339171, 210302171, 131649159046, 82254445109046, 51412313316921546, 32132285187903171546, 20082729571968536374671, 12551699566292514833249671, 7844813030956382105126218421 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

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 = 4..300

Index entries for linear recurrences with constant coefficients, signature (521,67730,-1693250,-8140625,9765625).

FORMULA

G.f.: -x^4 / ( (x-1)*(5*x+1)*(25*x-1)*(625*x-1)*(125*x+1) ). - R. J. Mathar, Aug 03 2016

MATHEMATICA

Table[QBinomial[n, 4, -5], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

PROG

(Sage) [gaussian_binomial(n, 4, -5) for n in xrange(4, 15)] # Zerinvary Lajos, May 27 2009

(MAGMA) r:=4; q:=-5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016

CROSSREFS

Sequence in context: A122715 A153180 A173656 * A028484 A057699 A033525

Adjacent sequences:  A015288 A015289 A015290 * A015292 A015293 A015294

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified March 25 12:11 EDT 2019. Contains 321470 sequences. (Running on oeis4.)