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%I #5 Mar 30 2012 18:37:34
%S 1,3,7,23,76,249,974,4151,16558,70308,342937,1680725,8012252,40903572,
%T 222539812,1202060807,6608077855,38523427818,228629565951,
%U 1349303611408,8257330774574,53118486147015,345693735519287,2252515985849693,15028013765653626,102689873016938288
%N L.g.f.: Sum_{n>=1} x^n/n * Product_{d|n} (1 + d*x^(n/d))^d.
%F Forms the logarithmic derivative of A205480.
%e L.g.f.: L(x) = x + 3*x^2/2 + 7*x^3/3 + 23*x^4/4 + 76*x^5/5 + 249*x^6/6 +...
%e By definition:
%e L(x) = x*(1+x) + x^2*(1+x^2)*(1+2*x)^2/2 + x^3*(1+x^3)*(1+3*x)^3/3 + x^4*(1+x^4)*(1+2*x^2)^2*(1+4*x)^4/4 + x^5*(1+x^5)*(1+5*x)^5/5 + x^6*(1+x^6)*(1+2*x^3)^2*(1+3*x^2)^3*(1+6*x)^6/6 +...
%e Exponentiation yields the g.f. of A205480:
%e exp(L(x)) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 27*x^5 + 76*x^6 + 242*x^7 +...
%o (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 Cf. A205480 (exp), A205477, A205479, A205483, A205485, A205487, A205489, A205491.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Jan 27 2012