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%I #7 Jul 04 2018 20:15:41
%S 1,2,6,10,26,42,86,130,258,386,694,1002,1754,2506,4134,5762,9346,
%T 12930,20198,27466,42330,57194,85750,114306,169602,224898,326934,
%U 428970,618138,807306,1144390,1481474,2084610,2687746,3732422,4777098,6591386
%N G.f.: A(x) = exp( 2*Sum_{n>=1} A006519(n)^2 * x^n/n ), where A006519(n) = highest power of 2 dividing n.
%H G. C. Greubel, <a href="/A162581/b162581.txt">Table of n, a(n) for n = 0..1000</a>
%e G.f.: A(x) = 1 + 2*x + 6*x^2 + 10*x^3 + 26*x^4 + 42*x^5 + 86*x^6 + ...
%e log(A(x))/2 = 2^0*x + 2^2*x^2 + 2^0*x^3/3 + 2^4*x^4/4 + 2^0*x^5/5 + 2^2*x^6/6 + 2^0*x^7/7 + 2^6*x^8/8 + ... + A006519(n)^2*x^n/n + ...
%t nmax = 200; a[n_]:= SeriesCoefficient[Series[Exp[ Sum[2^(2*IntegerExponent[k, 2] + 1)*q^k/k, {k, 1, nmax}]], {q,0,nmax}], n]; Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Jul 04 2018 *)
%o (PARI) {a(n)=local(L=sum(m=1,n,2*(2^valuation(m,2))^2*x^m/m)+x*O(x^n));polcoeff(exp(L),n)}
%Y Cf. A162580, A162582, A006519, A000123.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 06 2009
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