%I #7 Jul 04 2018 20:16:06

%S 1,4,10,24,52,112,240,512,1060,2192,4552,9440,19408,39872,81984,

%T 168448,342632,696736,1421200,2897856,5891872,11976064,24361856,

%U 49543168,100329952,203147136,411939264,835168512,1690383744,3420860928

%N G.f.: A(x) = exp( 2*Sum_{n>=1} 2^n/A006519(n) * x^n/n ), where A006519(n) = highest power of 2 dividing n.

%H G. C. Greubel, <a href="/A162588/b162588.txt">Table of n, a(n) for n = 0..1000</a>

%e G.f.: A(x) = 1 + 4*x + 10*x^2 + 24*x^3 + 52*x^4 + 112*x^5 + 240*x^6 + ...

%e log(A(x))/2 = 2*x + 2*x^2/2 + 8*x^3/3 + 4*x^4/4 + 32*x^5/5 + 32*x^6/6 + 128*x^7/7 + ...

%t nmax = 150; a[n_]:= SeriesCoefficient[Series[Exp[Sum[2^(k + 1 - IntegerExponent[k, 2])*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=2*sum(m=1,n,2^(m-valuation(m,2))*x^m/m)+x*O(x^n));polcoeff(exp(L),n)}

%Y Cf. A006519, A000123.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 07 2009