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

1, 45, 4335, 625725, 120423183, 28969886925, 8363051069055, 2816627967125325, 1084142007795994863, 469456525723134676365, 225871834295620808030175, 119542260051513982346194125, 69019118254891394556412984143

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Programs

Magma

m:=30; R:=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

Mathematica

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 *)
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 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(10-sum(k=1,9, exp(k*x))))) \\ G. C. Greubel, Oct 09 2018

Formula

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))