%I #10 Mar 16 2024 11:06:43
%S 1,0,2,3,176,1050,57144,744660,41682304,917959392,54654865920,
%T 1761420386880,113338947830976,4879197834619680,341937322823859840,
%U 18486700938579444480,1415296984669095859200,92017658919053166405120,7695907229874069158658048
%N E.g.f. satisfies A(x) = 1 - x*A(x)^4*log(1 - x*A(x)^3).
%F a(n) = (n!/(3*n+1)!) * Sum_{k=0..floor(n/2)} (3*n+k)! * |Stirling1(n-k,k)|/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n\2, (3*n+k)!*abs(stirling(n-k, k, 1))/(n-k)!)/(3*n+1)!;
%Y Cf. A370993, A371230.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 15 2024