A358014 Expansion of e.g.f. 1/(1 - x^3 * (exp(x) - 1)).
1, 0, 0, 0, 24, 60, 120, 210, 40656, 363384, 2117520, 9980190, 520250280, 9496208436, 109522054824, 982593614730, 28426015541280, 762523155318000, 14192088961120416, 204618562767970614, 4906638448867994040, 154037798077765359660, 4000484484370905087480
Offset: 0
Keywords
Programs
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Mathematica
With[{nn=30},CoefficientList[Series[1/(1-x^3 (Exp[x]-1)),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 26 2024 *) -
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^3*(exp(x)-1)))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=4, i, 1/(j-3)!*v[i-j+1]/(i-j)!)); v;
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PARI
a(n) = n!*sum(k=0, n\4, k!*stirling(n-3*k, k, 2)/(n-3*k)!);
Formula
a(0) = 1; a(n) = n! * Sum_{k=4..n} 1/(k-3)! * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/4)} k! * Stirling2(n-3*k,k)/(n-3*k)!.