%I #27 Sep 12 2022 03:05:25
%S 1,1,8,129,3188,106820,4530174,232744274,14054237000,975665799792,
%T 76568358325440,6703512043934112,647772783078516600,
%U 68484470168404178928,7863452609057425825704,974474039841523412062440,129636661193226128284609344,18427094124309886080021680640
%N E.g.f. satisfies: A(x) = 1/(1 - x * A(x)^2)^A(x).
%F a(n) = Sum_{k=0..n} (2*n+k+1)^(k-1) * |Stirling1(n,k)|.
%t m = 18; (* number of terms *)
%t A[_] = 0;
%t Do[A[x_] = 1/(1 - x*A[x]^2)^A[x] + 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, (2*n+k+1)^(k-1)*abs(stirling(n, k, 1)));
%Y Cf. A052813, A349556, A356960.
%Y Cf. A355766, A356972.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 07 2022
|