A015294 Gaussian binomial coefficient [ n,4 ] for q = -8.

1, 3641, 15150201, 61934287481, 253744775809657, 1039306892330748537, 4257017266254230145657, 17436734410124346225937017, 71420868399845502303592335993, 292539874786707389459461268654713

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..200

Index entries for linear recurrences with constant coefficients, signature (3641,1893320,-121172480,-954466304,1073741824).

Formula

G.f.: -x^4 / ( (x-1)*(4096*x-1)*(8*x+1)*(64*x-1)*(512*x+1) ). - R. J. Mathar, Aug 03 2016

Mathematica

Table[QBinomial[n, 4, -8], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Prog

(Sage) [gaussian_binomial(n, 4, -8) for n in range(4, 14)] # Zerinvary Lajos, May 27 2009
(Magma) r:=4; q:=-8; [&*[(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: A253491 A253452 A253464 * A186870 A185613 A232837

Adjacent sequences: A015291 A015292 A015293 * A015295 A015296 A015297

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved