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%I #6 May 24 2019 13:07:54
%S 1,1,2,4,16,56,256,1072,11264,119296,1075456,9088256,85292032,
%T 894690304,8968964096,90882789376,2409397682176,40515889528832,
%U 1051789297844224,16251803853193216,302342408330018816,4444559976664662016,84010278329827459072,1289319649553742823424
%N Expansion of e.g.f. exp(Sum_{k>=1} x^(k^2)*(2 + x^(k^2))/(2*k^2)).
%F E.g.f.: exp(Sum_{k>=1} A053866(k)*x^k/k).
%F E.g.f.: Product_{k>=1} 1/(1 - x^(2*k-1))^(lambda(2*k-1)/(2*k-1)), where lambda() is the Liouville function (A008836).
%t nmax = 23; CoefficientList[Series[Exp[Sum[x^(k^2) (2 + x^(k^2))/(2 k^2), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 23; CoefficientList[Series[Product[1/(1 - x^(2 k - 1))^(LiouvilleLambda[2 k - 1]/(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A008836, A053866, A205801, A306831.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, May 23 2019
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