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%I #11 Sep 11 2022 10:06:51
%S 1,0,2,6,50,510,5882,88326,1502258,29368590,650366762,15974149686,
%T 433095937826,12829712583870,412295632858202,14292175302568806,
%U 531485147656990994,21107739762958541550,891673745283286886282,39923664347178352362006
%N E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^2.
%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. A349588, A357087.
%Y Cf. A357084, A357088.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 11 2022
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