%I #10 Mar 16 2024 11:05:47
%S 1,0,2,3,128,750,29964,377160,15795072,329631120,15001287120,
%T 449174341440,22551082739712,885381886509120,49302509206648320,
%U 2391802812599316480,147728974730632012800,8502972330919072688640,580806950108814502345728
%N E.g.f. satisfies A(x) = 1 - x*A(x)^3*log(1 - x*A(x)^2).
%F a(n) = (n!/(2*n+1)!) * Sum_{k=0..floor(n/2)} (2*n+k)! * |Stirling1(n-k,k)|/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n\2, (2*n+k)!*abs(stirling(n-k, k, 1))/(n-k)!)/(2*n+1)!;
%Y Cf. A371227, A371228, A371229.
%Y Cf. A370993, A371232.
%Y Cf. A371122.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 15 2024