A004708 Expansion of 1/(11 - Sum_{k=1..10} exp(k*x)).

1, 55, 6435, 1128325, 263787183, 77087372725, 27032987762055, 11059911220828525, 5171317240313350863, 2720215076708542774405, 1589874326596159958849175, 1022150945200597388917580125

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/(11-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)-Exp(10*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Oct 09 2018

Mathematica

With[{nn=20},CoefficientList[Series[1/(11-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]-Exp[10*x]),{x,0,nn}],x] Range[0,nn]!] (* Vincenzo Librandi, Jun 15 2012 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(11-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)-exp(10*x)))) \\ G. C. Greubel, Oct 09 2018

Formula

Equals expansion of 1/(11-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)-exp(10*x)).