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E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1) * A(x)^3.
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%I #9 Nov 10 2023 08:18:43

%S 1,1,10,200,6167,258607,13748744,886397829,67211684890,5861684458896,

%T 578088714806497,63617223837958309,7728596914020856162,

%U 1027393177458209939977,148344954037140113652010,23119776330887635387231580,3868359765874829925197165527

%N E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1) * A(x)^3.

%F a(n) = Sum_{k=0..n} (n+3*k+1)^(k-1) * Stirling2(n,k).

%o (PARI) a(n) = sum(k=0, n, (n+3*k+1)^(k-1)*stirling(n, k, 2));

%Y Cf. A349525, A367163.

%Y Cf. A349557, A355762.

%Y Cf. A367199, A367200.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 10 2023