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A193200 G.f.: A(x) = Sum_{n>=0} x^n * Product_{d|n} (1 + x^d)^(n/d). 0

%I #5 Mar 30 2012 18:37:27

%S 1,1,2,3,6,10,17,32,54,92,170,311,555,986,1756,3100,5370,9295,16552,

%T 30535,57564,108830,202947,369829,659380,1162254,2053619,3675529,

%U 6683060,12293599,22697283,41734139,76077655,137460434,247056655,444239896,803916709

%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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