A004702 - OEIS

%I #20 Sep 08 2022 08:44:33

%S 1,10,230,7900,361754,20706700,1422295490,113976565300,10438383399674,

%T 1075482742196860,123120717545481650,15504276864309866500,

%U 2129906079562267271594,316979734672375940684620,50802750419531400066083810

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

%H Vincenzo Librandi, <a href="/A004702/b004702.txt">Table of n, a(n) for n = 0..200</a>

%F 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

%p 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

%t 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 *)

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

%o (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

%Y Column k=4 of A320253.

%K nonn

%O 0,2

%A _N. J. A. Sloane_