A004702 Expansion of e.g.f. 1/(5 - exp(x) - exp(2*x) - exp(3*x) - exp(4*x)).

1, 10, 230, 7900, 361754, 20706700, 1422295490, 113976565300, 10438383399674, 1075482742196860, 123120717545481650, 15504276864309866500, 2129906079562267271594, 316979734672375940684620, 50802750419531400066083810

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=4 of A320253.

Programs

Magma

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

Maple

seq(coeff(series(factorial(n)*(5-exp(x)-exp(2*x)-exp(3*x)-exp(4*x))^(-1),x,n+1), x, n), n = 0 .. 15); # Muniru A Asiru, Oct 10 2018

Mathematica

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

PARI

x='x+O('x^30); Vec(serlaplace(1/(5-sum(k=1,4, exp(k*x))))) \\ G. C. Greubel, Oct 09 2018

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (1 + 2^k + 3^k + 4^k) * a(n-k). - Ilya Gutkovskiy, Jan 15 2020