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%I #5 May 28 2019 19:29:27
%S 1,1,1,1,13,61,181,421,15961,137593,682921,2498761,77344741,927575221,
%T 6402167773,31881065581,4104839160241,68050288734961,609856397747281,
%U 3857727706737553,222655237411428541,4351842324095032621,47276537013742616581,361153046139022585141
%N Expansion of e.g.f. exp(x + 2 * Sum_{k>=2} x^(2^k)/2^k).
%F E.g.f.: Product_{k>=1} (1 + (-x)^k)^((-1)^k*mu(k)/k).
%F E.g.f.: exp(-x*(1 + x))*g(x)^2, where g(x) = e.g.f. of A005388.
%t nmax = 23; CoefficientList[Series[Exp[x + 2 Sum[x^(2^k)/2^k, {k, 2, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 23; CoefficientList[Series[Product[(1 + (-x)^k)^((-1)^k MoebiusMu[k]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A000321, A005388, A008683, A308392.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, May 28 2019
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