A004703 Expansion of e.g.f. 1/(6-exp(x)-exp(2*x)-exp(3*x)-exp(4*x)-exp(5*x)).

1, 15, 505, 25425, 1706629, 143195025, 14417768365, 1693616001225, 227365098508549, 34338804652192545, 5762408433135346525, 1063691250037869293625, 214198140845740727508469, 46728077502266943919186065

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (1 + 2^k + ... + 5^k) * a(n-k). - Ilya Gutkovskiy, Jan 15 2020

Mathematica

With[{nn=20}, CoefficientList[Series[1/(6-Exp[x]-Exp[2*x]-Exp[3*x] -Exp[4*x]-Exp[5*x]), {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Jun 14 2012 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(1/(6-sum(k=1, 5, exp(k*x))))) \\ G. C. Greubel, Oct 09 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(6-Exp(x)-Exp(2*x)-Exp(3*x)-Exp(4*x)-Exp(5*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Oct 09 2018

Crossrefs

Column k=5 of A320253.

Sequence in context: A219057 A203525 A249962 * A218188 A218365 A203326

Adjacent sequences: A004700 A004701 A004702 * A004704 A004705 A004706

Keyword

nonn

Author

N. J. A. Sloane

Status

approved