A192207 - OEIS

%I #8 Mar 30 2012 18:37:27

%S 1,1,3,8,25,79,268,931,3340,12221,45525,171932,657002,2535167,9864727,

%T 38663036,152491244,604788048,2410462518,9649584165,38782437824,

%U 156428161276,633003302363,2569122403034,10455470193615,42656724160734

%N G.f. A(x) satisfies A(x) = 1 + Sum_{n>=1} A(x)^n*x^n/(1 - x^n).

%F G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n * Sum_{d|n} A(x)^d.

%e G.f.: A(x) = 1 + x + 3*x^2 + 8*x^3 + 25*x^4 + 79*x^5 + 268*x^6 +...

%e which satisfies

%e A(x) = 1 + A(x)*x/(1-x) + A(x)^2*x^2/(1-x^2) + A(x)^3*x^3/(1-x^3) +...

%e The g.f. A = A(x) also satisfies

%e A = 1 + x*A + x^2*(A + A^2) + x^3*(A + A^3) + x^4*(A + A^2 + A^4) + x^5*(A + A^5) + x^6*(A + A^2 + A^3 + A^6) + x^7*(A + A^7) + x^8*(A + A^2 + A^4 + A^8) +...

%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*A^m/(1-x^m+x*O(x^n)))); polcoeff(A, n)}

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*sumdiv(m,d,A^d))+x*O(x^n));polcoeff(A,n)}

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 25 2011