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%I #17 Sep 12 2022 04:51:25
%S 1,0,0,6,36,210,3870,70224,1122072,23086344,586910880,15469437456,
%T 441107126856,14206113541152,496333927370736,18463733657766144,
%U 739328759822848320,31759148433997889280,1447876893211813379520,69881726567495477445120
%N E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2).
%F E.g.f. satisfies log(A(x)) = -log(1 - x * A(x))^3.
%F a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n+1)^(k-1) * |Stirling1(n,3*k)|/k!.
%t m = 20; (* number of terms *)
%t A[_] = 0;
%t Do[A[x_] = 1/(1 - x*A[x])^(Log[1 - x*A[x]]^2) + O[x]^m // Normal, {m}];
%t CoefficientList[A[x], x]*Range[0, m - 1]! (* _Jean-François Alcover_, Sep 12 2022 *)
%o (PARI) a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*abs(stirling(n, 3*k, 1))/k!);
%Y Cf. A001761, A357028.
%Y Cf. A353344, A357037.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 09 2022
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