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

%I A004706 #15 Sep 08 2022 08:44:33
%S A004706 1,36,2796,325296,50460324,9784339056,2276639188116,618021679767696,
%T A004706 191736660977760804,66920493102763469616,25951985825417984806836,
%U A004706 11070691364651231290738896,5151900329218737241490290884
%N A004706 Expansion of e.g.f. 1/(9 - Sum_{k=1..8} exp(k*x)).
%H A004706 Vincenzo Librandi, <a href="/A004706/b004706.txt">Table of n, a(n) for n = 0..200</a>
%F A004706 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)).
%F A004706 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
%t A004706 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 *)
%o A004706 (PARI) x='x+O('x^30); Vec(serlaplace(1/(9-sum(k=1,8, exp(k*x))))) \\ _G. C. Greubel_, Oct 09 2018
%o A004706 (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
%Y A004706 Column k=8 of A320253.
%K A004706 nonn
%O A004706 0,2
%A A004706 _N. J. A. Sloane_