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%I #14 Sep 12 2022 03:20:32
%S 1,0,2,6,82,820,13568,235368,5111748,123205248,3404436312,
%T 103998026880,3516027852456,129715202957184,5198615642907360,
%U 224652658604613120,10419411912935774736,516120552745366247424,27198524267826237745824
%N E.g.f. satisfies A(x) = (1 - x * A(x))^log(1 - x * A(x)).
%F E.g.f. satisfies log(A(x)) = log(1 - x * A(x))^2.
%F a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n+1)^(k-1) * |Stirling1(n,2*k)|/k!.
%t m = 20; (* number of terms *)
%t A[_] = 0;
%t Do[A[x_] = (1 - x*A[x])^Log[1 - x*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, (2*k)!*(n+1)^(k-1)*abs(stirling(n, 2*k, 1))/k!);
%Y Cf. A001761, A357029.
%Y Cf. A357036.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 09 2022
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