%I #10 Apr 23 2024 11:18:26
%S 1,4,40,688,17152,564864,23212288,1145627648,66082594816,
%T 4365282304000,325074868781056,26950224851927040,2462208223872286720,
%U 245811899064585814016,26626175172644096180224,3110339882223194198769664,389786352057654976473726976
%N E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) * (1 + A(x)^(1/2)) ).
%F E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A138764.
%F If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) * (1 + A(x)^(u/r)) ), then a(n) = r * Sum_{k=0..n} (t*n+u*k+r)^(n-1) * binomial(n,k).
%F a(n) = 2^n * A372177(n).
%o (PARI) a(n, r=2, t=1, u=1) = r*sum(k=0, n, (t*n+u*k+r)^(n-1)*binomial(n, k));
%Y Cf. A138764, A372177.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 23 2024