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%I #8 Mar 09 2024 08:16:24
%S 1,0,0,6,24,60,1560,25410,242256,3508344,85882320,1724406750,
%T 32784999720,839182482996,24162605028744,659439484706730,
%U 19415319297457440,658935736181053680,23245444335085544736,835819877947421773494,32462532011236141677240
%N E.g.f. satisfies A(x) = 1 + x^3*A(x)^2*exp(x*A(x)).
%F a(n) = n! * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n-k+1,k)/( (n-k+1)*(n-3*k)! ).
%o (PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n-k+1, k)/((n-k+1)*(n-3*k)!));
%Y Cf. A370985, A371019, A371044, A371045.
%Y Cf. A365286.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Mar 09 2024
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