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A004707 Expansion of 1/(10 - Sum_{k=1..9} exp(k*x)).

%I A004707 #13 Sep 08 2022 08:44:33
%S A004707 1,45,4335,625725,120423183,28969886925,8363051069055,
%T A004707 2816627967125325,1084142007795994863,469456525723134676365,
%U A004707 225871834295620808030175,119542260051513982346194125,69019118254891394556412984143
%N A004707 Expansion of 1/(10 - Sum_{k=1..9} exp(k*x)).
%H A004707 Vincenzo Librandi, <a href="/A004707/b004707.txt">Table of n, a(n) for n = 0..200</a>
%F A004707 Equals expansion of 1/(10-exp(x)-exp(2*x)-exp(3*x)-exp(4*x)-exp(5*x)-exp(6*x)-exp(7*x)-exp(8*x)-exp(9*x))
%t A004707 With[{nn=200},CoefficientList[Series[1/(10-Exp[x]-Exp[2*x]-Exp[3*x]-Exp[4*x]-Exp[5*x]-Exp[6*x]-Exp[7*x]-Exp[8*x]-Exp[9*x]),{x,0,nn}],x] Range[0,nn]!] (* _Vincenzo Librandi_, Jun 15 2012 *)
%t A004707 With[{nn=20},CoefficientList[Series[1/(10-Total[Table[Exp[n*x],{n,9}]]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 15 2015 *)
%o A004707 (PARI) x='x+O('x^30); Vec(serlaplace(1/(10-sum(k=1,9, exp(k*x))))) \\ _G. C. Greubel_, Oct 09 2018
%o A004707 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(10-Exp(x)-Exp(2*x)-Exp(3*x)-Exp(4*x)-Exp(5*x)-Exp(6*x)-Exp(7*x)-Exp(8*x)-Exp(9*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Oct 09 2018
%K A004707 nonn
%O A004707 0,2
%A A004707 _N. J. A. Sloane_