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%I #5 Mar 30 2012 18:37:34
%S 1,3,4,15,31,72,176,327,751,2063,5138,12708,30993,75386,182644,433255,
%T 1004854,2279349,5115960,11580835,26533616,62024966,149683357,
%U 373141332,957942931,2516465279,6694846987,17883365774,47644695777,125952933062,329364348277
%N L.g.f.: Sum_{n>=1} x^n/n * Product_{d|n} (1 + d*x^d)^n.
%F Forms the logarithmic derivative of A205484.
%e L.g.f.: L(x) = x + 3*x^2/2 + 4*x^3/3 + 15*x^4/4 + 31*x^5/5 + 72*x^6/6 +...
%e By definition:
%e L(x) = x*(1+x) + x^2*(1+x)^2*(1+2*x^2)^2/2 + x^3*(1+x)^3*(1+3*x^3)^3/3 + x^4*(1+x)^4*(1+2*x^2)^4*(1+4*x^4)^4/4 + x^5*(1+x)^5*(1+5*x^5)^5/5 + x^6*(1+x)^6*(1+2*x^2)^6*(1+3*x^3)^6*(1+6*x^6)^6/6 +...
%e Exponentiation yields the g.f. of A205484:
%e exp(L(x)) = 1 + x + 2*x^2 + 3*x^3 + 7*x^4 + 14*x^5 + 30*x^6 + 65*x^7 +...
%o (PARI) {a(n)=n*polcoeff(sum(m=1, n+1, x^m/m*exp(sumdiv(m, d, m*log(1+d*x^d+x*O(x^n))))), n)}
%Y Cf. A205484 (exp), A205477, A205479, A205481, A205483, A205487, A205489, A205491.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Jan 27 2012
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