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

0,2

Links

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

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

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 *)

Prog

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

Crossrefs

Column k=7 of A320253.

Sequence in context: A339120 A194190 A190397 * A182400 A333125 A197438

Adjacent sequences: A004702 A004703 A004704 * A004706 A004707 A004708

Keyword

nonn

Author

N. J. A. Sloane

Status

approved