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Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^4 / 576).
4

%I #11 May 09 2022 15:19:53

%S 1,0,0,0,0,0,0,0,70,1260,13650,115500,841995,5555550,34139105,

%T 198948750,1175994820,10315705400,192609389700,4563951046200,

%U 98992258506345,1898260633492650,32787422848455275,520556451785466250,7722233521138092726,108688302800107222500

%N Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^4 / 576).

%F a(n) = n! * Sum_{k=0..floor(n/8)} (4*k)! * Stirling2(n-4*k,4*k)/(576^k * (n-4*k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(x*(exp(x)-1))^4/576)))

%o (PARI) a(n) = n!*sum(k=0, n\8, (4*k)!*stirling(n-4*k, 4*k, 2)/(576^k*(n-4*k)!));

%Y Cf. A052848, A353883, A353884.

%Y Cf. A346895, A353882.

%K nonn

%O 0,9

%A _Seiichi Manyama_, May 09 2022