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Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^3 / 36).
4

%I #12 May 09 2022 15:19:40

%S 1,0,0,0,0,0,20,210,1400,7560,36120,159390,1035100,17082780,329893564,

%T 5336661330,73265956400,889068944400,9968073461616,112902000191334,

%U 1531070090032500,27610559023112100,586336131631313140,12550716321612658266,254052845940651258600

%N Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^3 / 36).

%F a(n) = n! * Sum_{k=0..floor(n/6)} (3*k)! * Stirling2(n-3*k,3*k)/(36^k * (n-3*k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(x*(exp(x)-1))^3/36)))

%o (PARI) a(n) = n!*sum(k=0, n\6, (3*k)!*stirling(n-3*k, 3*k, 2)/(36^k*(n-3*k)!));

%Y Cf. A052848, A353883, A353885.

%Y Cf. A346894, A353881.

%K nonn

%O 0,7

%A _Seiichi Manyama_, May 09 2022