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%I #7 Mar 12 2024 09:33:21
%S 1,0,2,3,76,365,9906,94507,2832824,43209945,1438766830,30971280791,
%T 1146868043124,32166137748901,1322928667341386,45791799761422275,
%U 2085517396191903856,85748423669245738673,4306944218393176448742,204597526239295278145327
%N E.g.f. satisfies A(x) = 1 + x*A(x)^3 * (exp(x) - 1).
%F a(n) = n! * Sum_{k=0..floor(n/2)} (3*k)!/(2*k+1)! * Stirling2(n-k,k)/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n\2, (3*k)!/(2*k+1)!*stirling(n-k, k, 2)/(n-k)!);
%Y Cf. A052848, A371142.
%Y Cf. A371141.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 12 2024