%I #10 Mar 09 2024 08:14:53
%S 1,0,2,6,36,380,3630,47082,725816,12132360,235801530,5083309550,
%T 119757623172,3103443520476,87082536196838,2632399338834930,
%U 85471932351187440,2961803643600574352,109154615479427298546,4264407640037365789014,175984871341042826680700
%N E.g.f. satisfies A(x) = 1 + x^2*A(x)*exp(x*A(x)).
%F a(n) = n! * Sum_{k=0..floor(n/2)} k^(n-2*k) * binomial(n-k+1,k)/( (n-k+1)*(n-2*k)! ).
%o (PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)*binomial(n-k+1, k)/((n-k+1)*(n-2*k)!));
%Y Cf. A370984, A371018, A371042.
%Y Cf. A365282.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 09 2024