%I #9 Mar 17 2024 04:07:38
%S 1,0,2,3,172,1025,54606,710017,38964024,855167553,49992166090,
%T 1603665906161,101454726848388,4342187407054081,299554876119595110,
%U 16084216120063348545,1213404824364026124016,78279943651487041769345,6456915976418046368634402
%N E.g.f. satisfies A(x) = 1 + x*A(x)^4 * (exp(x*A(x)^3) - 1).
%F a(n) = (n!/(3*n+1)!) * Sum_{k=0..floor(n/2)} (3*n+k)! * Stirling2(n-k,k)/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n\2, (3*n+k)!*stirling(n-k, k, 2)/(n-k)!)/(3*n+1)!;
%Y Cf. A370988, A371271.
%Y Cf. A371232.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 16 2024