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%I
%S 1,0,0,6,36,210,4590,85344,1353912,30525384,836587440,22585438656,
%T 676820305656,23377203675072,857981143380816,33416782099297344,
%U 1417453025671696320,64371985604089220160,3086958605328618687360,157142856384519974847360
%N E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2 * A(x)).
%F E.g.f. satisfies log(A(x)) = -log(1 - x * A(x))^3 * A(x).
%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. A349556, A357090.
%Y Cf. A357029.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 11 2022
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