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A205491 L.g.f.: Sum_{n>=1} (x^n/n) / Product_{d|n} (1 - d*x^d)^n.

%I A205491 #5 Mar 30 2012 18:37:34
%S A205491 1,3,7,23,51,165,386,1039,2554,6963,17260,47825,124840,340658,911037,
%T A205491 2484687,6614616,17735646,46647167,122536323,318125129,825153684,
%U A205491 2130076369,5522611009,14375957026,37817347272,100579846732,271246531726,740731197176
%N A205491  L.g.f.: Sum_{n>=1} (x^n/n) / Product_{d|n} (1 - d*x^d)^n.
%F A205491  Forms the logarithmic derivative of A205490.
%e A205491  L.g.f.: L(x) = x + 3*x^2/2 + 7*x^3/3 + 23*x^4/4 + 51*x^5/5 + 165*x^6/6 +...
%e A205491 By definition:
%e A205491 L(x) = x/(1-x) + (x^2/2)/((1-x)^2*(1-2*x^2)^2) + (x^3/3)/((1-x)^3*(1-3*x^3)^3) + (x^4/4)/((1-x)^4*(1-2*x^2)^4*(1-4*x^4)^4) + (x^5/5)/((1-x)^5*(1-5*x^5)^5) + (x^6/6)/((1-x)^6*(1-2*x^2)^6*(1-3*x^3)^6*(1-6*x^6)^6) +...
%e A205491 Exponentiation yields the g.f. of A205490:
%e A205491 exp(L(x)) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 22*x^5 + 57*x^6 + 134*x^7 +...
%o A205491  (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 A205491  Cf. A205490 (exp), A205477, A205479, A205481, A205483, A205485, A205487, A205489.
%K A205491 nonn
%O A205491 1,2
%A A205491 _Paul D. Hanna_, Jan 27 2012