%I #9 Mar 10 2024 07:50:35
%S 1,1,0,0,24,360,2160,7560,241920,8164800,145756800,1736380800,
%T 34488115200,1416906691200,46117316044800,1085696644032000,
%U 26627911620710400,1054301997805056000,46867776416068608000,1726488804870679449600,58404671366139850752000
%N E.g.f. satisfies A(x) = 1 + x*exp(x^3*A(x)^3).
%F a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)^k * binomial(3*k+1,n-3*k)/( (3*k+1)*k! ).
%o (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k*binomial(3*k+1, n-3*k)/((3*k+1)*k!));
%Y Cf. A365287, A370928.
%Y Cf. A161631, A371067.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Mar 09 2024