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A380771 E.g.f. A(x) satisfies A(x) = exp(x * A(x) * (1 + x*A(x)^2)) * (1 + x*A(x)^2).

%I A380771 #10 Feb 03 2025 11:07:36
%S A380771 1,2,17,277,6797,224301,9327235,468615379,27624235385,1869871826521,
%T A380771 142960839681311,12185757382882623,1145898471300898837,
%U A380771 117849030630765668677,13159165724143312996907,1585485015346749680509051,205026978076680944633853425,28324382622872897021731667121
%N A380771 E.g.f. A(x) satisfies A(x) = exp(x * A(x) * (1 + x*A(x)^2)) * (1 + x*A(x)^2).
%F A380771 a(n) = n! * Sum_{k=0..n} (2*n-k+1)^(k-1) * binomial(2*n+1,n-k)/k!.
%o A380771 (PARI) a(n, q=1, r=2, s=1, t=1, u=1) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial(r*u*n+((s-r)*u+t)*k+q*u, n-k)/k!);
%Y A380771 Cf. A380768.
%K A380771 nonn
%O A380771 0,2
%A A380771 _Seiichi Manyama_, Feb 02 2025