cp's OEIS Frontend

A205487 L.g.f.: Sum_{n>=1} (x^n/n) / Product_{d|n} (1 - d*x^(n/d))^d.

%I A205487 #8 Apr 15 2025 18:51:05
%S A205487 1,3,10,43,206,1104,6581,43227,307927,2351288,19124238,165102052,
%T A205487 1507907818,14512524085,146581677005,1548261405595,17054944088112,
%U A205487 195518380169283,2328512358930925,28759349826041248,367752208054445945,4860792910118985370
%N A205487 L.g.f.: Sum_{n>=1} (x^n/n) / Product_{d|n} (1 - d*x^(n/d))^d.
%F A205487 Forms the logarithmic derivative of A205486.
%e A205487 L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 206*x^5/5 + 1104*x^6/6 +...
%e A205487 By definition:
%e A205487 L(x) = x/(1-x) + (x^2/2)/((1-x^2)*(1-2*x)^2) + (x^3/3)/((1-x^3)*(1-3*x)^3) + (x^4/4)/((1-x^4)*(1-2*x^2)^2*(1-4*x)^4) + (x^5/5)/((1-x^5)*(1-5*x)^5) + (x^6/6)/((1-x^6)*(1-2*x^3)^2*(1-3*x^2)^3*(1-6*x)^6) +...
%e A205487 Exponentiation yields the g.f. of A205486:
%e A205487 exp(L(x)) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 60*x^5 + 259*x^6 + 1273*x^7 +...
%o A205487 (PARI) {a(n)=n*polcoeff(sum(m=1, n+1, x^m/m*exp(sumdiv(m, d, -d*log(1-d*x^(m/d)+x*O(x^n))))), n)}
%Y A205487 Cf. A205486 (exp), A205477, A205479, A205481, A205483, A205485, A205489, A205491.
%K A205487 nonn
%O A205487 1,2
%A A205487 _Paul D. Hanna_, Jan 27 2012