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%I #7 Jul 04 2018 22:18:59
%S 1,2,6,12,38,76,188,376,1094,2188,5236,10472,26076,52152,118840,
%T 237680,612678,1225356,2804420,5608840,13279604,26559208,59074504,
%U 118149008,277925148,555850296,1228260104,2456520208,5552652792,11105305584
%N G.f.: A(x) = exp( 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="/A162589/b162589.txt">Table of n, a(n) for n = 0..1000</a>
%e G.f.: A(x) = 1 + 2*x + 6*x^2 + 12*x^3 + 38*x^4 + 76*x^5 + 188*x^6 + ...
%e log(A(x)) = 2*x + 8*x^2/2 + 8*x^3/3 + 64*x^4/4 + 32*x^5/5 + 128*x^6/6 + 128*x^7/7 + ...
%t nmax = 150; a[n_]:= SeriesCoefficient[Series[Exp[Sum[2^(k + 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=sum(m=1,n,2^(m+valuation(m,2))*x^m/m)+x*O(x^n));polcoeff(exp(L),n)}
%Y Cf. A162588, A006519, A000123.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 07 2009
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