%I #9 Sep 11 2022 10:06:30

%S 1,0,2,6,98,990,19082,347046,8512226,220737390,6776521082,

%T 225532370646,8413133799314,339965749171230,14995100013227882,

%U 711308930246853126,36278600375671552322,1974411768891211652430,114394542828023045764442

%N E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1)^2 * A(x).

%F a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n+k+1)^(k-1) * Stirling2(n,2*k)/k!.

%o (PARI) a(n) = sum(k=0, n\2, (2*k)!*(n+k+1)^(k-1)*stirling(n, 2*k, 2)/k!);

%Y Cf. A349557, A357085.

%Y Cf. A357024.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 11 2022