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%I #10 Sep 11 2022 10:07:33
%S 1,0,2,6,106,1060,21728,396648,10174764,267855264,8517836832,
%T 289596897480,11137252365600,461124747706896,20922578332613904,
%U 1018268757357253920,53372000211252229392,2981808910524462942720,177468245487057424475136
%N E.g.f. satisfies A(x) = (1 - x * A(x))^(log(1 - x * A(x)) * A(x)).
%F E.g.f. satisfies log(A(x)) = log(1 - x * A(x))^2 * A(x).
%F a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n+k+1)^(k-1) * |Stirling1(n,2*k)|/k!.
%o (PARI) a(n) = sum(k=0, n\2, (2*k)!*(n+k+1)^(k-1)*abs(stirling(n, 2*k, 1))/k!);
%Y Cf. A349556, A357091.
%Y Cf. A357028.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 11 2022
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