A004704 Expansion of e.g.f. 1/(7- Sum_{k=1..6} exp(k*x)).

1, 21, 973, 67473, 6238309, 720964881, 99986786773, 16177741934193, 2991473373828709, 622307309978695761, 143840821212045590773, 36572284571798550251313, 10144031468802588684994309, 3048113900510603294243693841

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=6 of A320253.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(7-Exp(x)-Exp(2*x)-Exp(3*x)-Exp(4*x)-Exp(5*x)-Exp(6*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Oct 09 2018

Mathematica

With[{nn=20},CoefficientList[Series[1/(7-Exp[x]-Exp[2*x]-Exp[3*x]-Exp[4*x]-Exp[5*x]-Exp[6*x]),{x,0,nn}],x] Range[0,nn]!] (* Vincenzo Librandi, Jun 14 2012 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(7-sum(k=1,6, exp(k*x))))) \\ G. C. Greubel, Oct 09 2018

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (1 + 2^k + ... + 6^k) * a(n-k). - Ilya Gutkovskiy, Jan 15 2020