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%I #10 Jul 16 2022 11:49:56
%S 1,1,6,77,1533,41547,1427789,59501185,2916185862,164377512831,
%T 10477134939301,745130845917317,58499605416732225,5025399546258317683,
%U 468897159717886522970,47222645752129576973609,5105611277081800029406545,589843003782904742592169479
%N E.g.f. satisfies log(A(x)) = (1 - exp(-x*A(x))) * A(x)^2.
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * (n+2*k+1)^(k-1) * Stirling2(n,k).
%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*(n+2*k+1)^(k-1)*stirling(n, k, 2));
%Y Cf. A334986, A349558.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jul 16 2022