%I #10 Sep 11 2022 10:08:04
%S 1,0,0,6,36,210,3150,55104,890232,16735944,386223120,9790441056,
%T 265867900056,7943197796352,260063260578576,9156071916788544,
%U 344740627648393920,13880862578534022720,595178180505073088640,27035591386823290224000
%N E.g.f. satisfies A(x)^A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2).
%F E.g.f. satisfies A(x) * log(A(x)) = -log(1 - x * A(x))^3.
%F a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n-k+1)^(k-1) * |Stirling1(n,3*k)|/k!.
%o (PARI) a(n) = sum(k=0, n\3, (3*k)!*(n-k+1)^(k-1)*abs(stirling(n, 3*k, 1))/k!);
%Y Cf. A141209, A357092.
%Y Cf. A357029.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 11 2022
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