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

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=5 of A320253.

Programs

Magma

m:=30; R:=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

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 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(6-sum(k=1,5, exp(k*x))))) \\ G. C. Greubel, Oct 09 2018

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