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%I #10 Aug 31 2023 08:16:43
%S 1,1,2,6,48,480,5040,57960,806400,13426560,250992000,5102697600,
%T 113283878400,2760905347200,73287883468800,2093750122464000,
%U 63947194517606400,2082970788291993600,72182922107859763200,2651026034089585152000
%N E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^3*A(x)).
%F a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)^k * binomial(n-2*k+1,n-3*k)/( (n-2*k+1)*k! ).
%o (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k*binomial(n-2*k+1, n-3*k)/((n-2*k+1)*k!));
%Y Cf. A358065, A365286, A365287.
%Y Cf. A365282.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 31 2023
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