%I #16 Jul 06 2024 12:35:08
%S 1,2,6,20,88,432,2464,14912,111360,912896,8491264,80905728,861835264,
%T 9524264960,113218762752,1362387243008,20665650774016,337892698226688,
%U 6100999266304000,106342541313572864,2014622956858638336,37864490015441027072
%N E.g.f. A(x) satisfies A(x) = A(x^2)^(1/2) * exp(2*x) with A(0)=1.
%H Seiichi Manyama, <a href="/A374346/b374346.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: exp( 2 * Sum_{k>=0} x^(2^k)/2^k ).
%F E.g.f.: 1/( Product_{k>=1} (1 - x^(2*k-1))^(mu(2*k-1)/(2*k-1)) )^2, where mu() is the Moebius function.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*sum(k=0, ceil(log(N+1)/log(2)), x^2^k/2^k))))
%Y Cf. A005388, A008683, A118393, A308392.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Jul 05 2024