%I #7 Apr 20 2021 19:13:48
%S 1,1,2,4,9,18,39,81,170,355,748,1576,3334,7054,14935,31591,66732,
%T 140708,296379,624389,1317807,2790095,5930254,12652077,27071714,
%U 58019282,124377335,266404590,569755992,1216513200,2593884456,5526424017,11773433242
%N G.f.: A(x) = Sum_{n>=0} x^n / Product_{d|n} (1 - x^d)^(n/d).
%e G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 9*x^5 + 20*x^6 + 31*x^7 + ...
%e where:
%e A(x) = 1 + x/(1-x) + x^2/((1-x)^2*(1-x^2)) + x^3/((1-x)^3*(1-x^3)) + x^4/((1-x)^4*(1-x^2)^2*(1-x^4)) + x^5/((1-x)^5*(1-x^5)) + x^6/((1-x)^6*(1-x^2)^3*(1-x^3)^2*(1-x^6)) + ...
%o (PARI) {a(n)=local(A=1);A=1+sum(m=1,n,x^m/prod(d=1,m,if(m%d==0,(1-x^d +x*O(x^n))^(m/d),1)));polcoeff(A,n)}
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 17 2011
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