%I #10 Mar 16 2024 11:56:14
%S 1,0,2,3,152,930,42804,574140,27267456,613793376,31378237200,
%T 1021391030880,57256014687552,2456525677525920,152135168050833408,
%U 8093376365276966400,554533365688970342400,35081649646969248529920,2653840371674014197608448
%N E.g.f. satisfies A(x) = 1 - x*A(x)^3*log(1 - x*A(x)^3).
%F a(n) = n! * (3*n)! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/( (n-k)! * (3*n-k+1)! ).
%o (PARI) a(n) = n!*(3*n)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(3*n-k+1)!));
%Y Cf. A371121, A371229.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 15 2024