This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A205485 #8 Aug 22 2025 17:57:39
%S A205485 1,3,4,15,31,72,176,327,751,2063,5138,12708,30993,75386,182644,433255,
%T A205485 1004854,2279349,5115960,11580835,26533616,62024966,149683357,
%U A205485 373141332,957942931,2516465279,6694846987,17883365774,47644695777,125952933062,329364348277
%N A205485 L.g.f.: Sum_{n>=1} x^n/n * Product_{d|n} (1 + d*x^d)^n.
%F A205485 Forms the logarithmic derivative of A205484.
%e A205485 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 A205485 By definition:
%e A205485 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 A205485 Exponentiation yields the g.f. of A205484:
%e A205485 exp(L(x)) = 1 + x + 2*x^2 + 3*x^3 + 7*x^4 + 14*x^5 + 30*x^6 + 65*x^7 +...
%o A205485 (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 A205485 Cf. A205484 (exp), A205477, A205479, A205481, A205483, A205487, A205489, A205491.
%K A205485 nonn
%O A205485 1,2
%A A205485 _Paul D. Hanna_, Jan 27 2012