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%I #8 Aug 15 2023 07:45:28
%S 1,1,8,123,2884,91445,3664926,177796759,10132646840,663644108169,
%T 49123993335130,4055804550134051,369544757016476196,
%U 36834870020525413213,3987179241476814768854,465777171342934543710255,58407238852473276959363056,7825395596421876706944643985
%N E.g.f. satisfies A(x) = 1 + x*A(x)^3*exp(x*A(x)^2).
%F a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(2*n+k+1,k)/( (2*n+k+1)*(n-k)! ).
%o (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(2*n+k+1, k)/((2*n+k+1)*(n-k)!));
%Y Cf. A364983, A364984, A364986.
%Y Cf. A003168.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 15 2023
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