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A015289 Gaussian binomial coefficient [ n,4 ] for q = -4. 3
1, 205, 55965, 14107485, 3625623645, 927257668701, 237435704507485, 60779845138496605, 15559876852907031645, 3983313338565919030365, 1019729183363623510391901, 261050608944894743386831965 (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..400

Index entries for linear recurrences with constant coefficients, signature (205,13940,-223040,-839680,1048576).

FORMULA

G.f.: -x^4 / ( (x-1)*(256*x-1)*(64*x+1)*(4*x+1)*(16*x-1) ). - R. J. Mathar, Aug 03 2016

MATHEMATICA

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

PROG

(Sage) [gaussian_binomial(n, 4, -4) for n in xrange(4, 16)] # Zerinvary Lajos, May 27 2009

(MAGMA) r:=4; q:=-4; [&*[(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: A060892 A203862 A289333 * A203888 A188447 A252278

Adjacent sequences:  A015286 A015287 A015288 * A015290 A015291 A015292

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified March 23 05:36 EDT 2019. Contains 321422 sequences. (Running on oeis4.)