OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
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
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 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(1/(5-sum(k=1, 4, exp(k*x))))) \\ G. C. Greubel, Oct 09 2018
(Magma) m:=30; R<x>:=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
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved