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%I #9 Nov 01 2024 09:30:10
%S 1,2,10,114,2000,47050,1399452,50386406,2130643216,103530094866,
%T 5684985037460,348165567064942,23530146364469208,1739586913373486138,
%U 139658209205202262876,12099843726478251739830,1125274333255817053205792,111809642081518362872011042,11821367007844973309548419876
%N E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)^2))^2.
%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377550.
%F a(n) = 2 * n! * Sum_{k=0..n} k^(n-k) * binomial(4*n-3*k+2,k)/( (4*n-3*k+2)*(n-k)! ).
%o (PARI) a(n) = 2*n!*sum(k=0, n, k^(n-k)*binomial(4*n-3*k+2, k)/((4*n-3*k+2)*(n-k)!));
%Y Cf. A377550, A377551.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 31 2024