%I #17 Sep 12 2022 03:04:27

%S 1,0,0,1,6,35,295,3304,42112,599724,9657330,174222576,3464835726,

%T 75208002792,1771121398956,44998593873024,1226723273550720,

%U 35714547582173280,1106012915718532920,36304411160854523520,1259105580819317636280,46007354360033491345920

%N E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2 / 6).

%F E.g.f. satisfies log(A(x)) = -log(1 - x * A(x))^3 / 6.

%F a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n+1)^(k-1) * |Stirling1(n,3*k)|/(6^k * k!).

%t m = 22; (* number of terms *)

%t A[_] = 0;

%t Do[A[x_] = 1/(1 - x*A[x])^(Log[1 - x*A[x]]^2/6) + O[x]^m // Normal, {m}];

%t CoefficientList[A[x], x]*Range[0, m - 1]! (* _Jean-François Alcover_, Sep 12 2022 *)

%o (PARI) a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*abs(stirling(n, 3*k, 1))/(6^k*k!));

%Y Cf. A001761, A357036.

%Y Cf. A347002, A357029, A357032.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Sep 09 2022