A374346 E.g.f. A(x) satisfies A(x) = A(x^2)^(1/2) * exp(2*x) with A(0)=1.
1, 2, 6, 20, 88, 432, 2464, 14912, 111360, 912896, 8491264, 80905728, 861835264, 9524264960, 113218762752, 1362387243008, 20665650774016, 337892698226688, 6100999266304000, 106342541313572864, 2014622956858638336, 37864490015441027072
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..200
Programs
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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))))
Formula
E.g.f.: exp( 2 * Sum_{k>=0} x^(2^k)/2^k ).
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.