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E.g.f. A(x) satisfies A(x) = A(x^2)^(1/2) * exp(2*x) with A(0)=1.
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%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