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%I
%S 1,0,0,1,6,35,275,2884,35672,494724,7673670,132896676,2544253426,
%T 53252983992,1208888367596,29592833903424,777311220788320,
%U 21808542026480120,650880782773059840,20590135175285212800,688212821908314587880,24235789570607605377680
%N E.g.f. satisfies A(x)^A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2 / 6).
%F E.g.f. satisfies A(x) * log(A(x)) = -log(1 - x * A(x))^3 / 6.
%F a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n-k+1)^(k-1) * |Stirling1(n,3*k)|/(6^k * k!).
%o (PARI) a(n) = sum(k=0, n\3, (3*k)!*(n-k+1)^(k-1)*abs(stirling(n, 3*k, 1))/(6^k*k!));
%Y Cf. A141209, A357094.
%Y Cf. A357037.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Sep 11 2022
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