A004706 Expansion of e.g.f. 1/(9 - Sum_{k=1..8} exp(k*x)).

1, 36, 2796, 325296, 50460324, 9784339056, 2276639188116, 618021679767696, 191736660977760804, 66920493102763469616, 25951985825417984806836, 11070691364651231290738896, 5151900329218737241490290884

Offset

0,2

Links

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

Formula

Equals expansion of e.g.f. 1/(9-exp(x)-exp(2*x)-exp(3*x)-exp(4*x)-exp(5*x)-exp(6*x)-exp(7*x)-exp(8*x)).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (1 + 2^k + ... + 8^k) * a(n-k). - Ilya Gutkovskiy, Jan 15 2020

Mathematica

With[{nn=20}, CoefficientList[Series[1/(9-Exp[x]-Exp[2*x]-Exp[3*x]-Exp[4*x]-Exp[5*x]-Exp[6*x]-Exp[7*x]-Exp[8*x]), {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Jun 15 2012 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(1/(9-sum(k=1, 8, exp(k*x))))) \\ G. C. Greubel, Oct 09 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(9-Exp(x)-Exp(2*x)-Exp(3*x)-Exp(4*x)-Exp(5*x)-Exp(6*x)-Exp(7*x)-Exp(8*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Oct 09 2018

Crossrefs

Column k=8 of A320253.

Sequence in context: A198639 A159728 A268365 * A061844 A036510 A232669

Adjacent sequences: A004703 A004704 A004705 * A004707 A004708 A004709

Keyword

nonn

Author

N. J. A. Sloane

Status

approved