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%I #8 Aug 15 2023 07:41:57
%S 1,1,2,21,220,3545,70566,1702267,48438104,1582227873,58475787850,
%T 2410935939731,109728296017572,5464423604085745,295562179335075758,
%U 17255009243888243115,1081438061864539992496,72422934220506772042817,5161269584065131270532242
%N E.g.f. satisfies A(x) = 1 + x*exp(x*A(x)^3).
%F a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(3*n-3*k+1,k)/( (3*n-3*k+1)*(n-k)! ).
%o (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(3*n-3*k+1, k)/((3*n-3*k+1)*(n-k)!));
%Y Cf. A161631, A364978.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 15 2023
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