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%I #20 Sep 08 2022 08:44:33
%S 1,6,86,1836,52250,1858716,79345346,3951633636,224917803770,
%T 14402023566156,1024662142371506,80191908540219636,
%U 6846505625682597290,633241684193651067996,63074628985206471485666,6731364953866743063784836
%N Expansion of e.g.f. 1/(4 - exp(x) - exp(2*x) - exp(3*x)).
%H Vincenzo Librandi, <a href="/A004701/b004701.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) * a(n-k). - _Ilya Gutkovskiy_, Jan 15 2020
%p seq(coeff(series(factorial(n)*(4-exp(x)-exp(2*x)-exp(3*x))^(-1),x,n+1), x, n), n = 0 .. 15); # _Muniru A Asiru_, Oct 10 2018
%t With[{nn=20},CoefficientList[Series[1/(4-Exp[x]-Exp[2*x]-Exp[3*x]),{x,0,nn}],x] Range[0,nn]!] (* _Vincenzo Librandi_, Jun 14 2012 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(1/(4-sum(k=1,3, exp(k*x))))) \\ _G. C. Greubel_, Oct 09 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(4-Exp(x)-Exp(2*x)-Exp(3*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Oct 09 2018
%Y Column k=3 of A320253.
%K nonn
%O 0,2
%A _N. J. A. Sloane_