A004705 Expansion of e.g.f. 1/(8 - Sum_{k=1..7} exp(k*x)).

1, 28, 1708, 156016, 19000996, 2892636208, 528436162708, 112625837135056, 27433137537640996, 7517361789179684848, 2288826715171726889908, 766572192067000875962896, 280079787805796188648857796, 110859415083883527695265783088

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=7 of A320253.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(8-Exp(x)-Exp(2*x)-Exp(3*x)-Exp(4*x)-Exp(5*x)-Exp(6*x)-Exp(7*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Oct 09 2018

Mathematica

With[{nn=200},CoefficientList[Series[1/(8-Exp[x]-Exp[2*x]-Exp[3*x]-Exp[4*x]-Exp[5*x]-Exp[6*x]-Exp[7*x]),{x,0,nn}],x] Range[0,nn]!] (* Vincenzo Librandi, Jun 15 2012 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(8-sum(k=1,7, exp(k*x))))) \\ G. C. Greubel, Oct 09 2018

Formula

Equals expansion of e.g.f. 1/(8-exp(x)-exp(2*x)-exp(3*x)-exp(4*x)-exp(5*x)-exp(6*x)-exp(7*x)).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (1 + 2^k + ... + 7^k) * a(n-k). - Ilya Gutkovskiy, Jan 15 2020