A206302 - OEIS

%I #7 Mar 30 2012 18:37:35

%S 1,1,2,5,15,45,147,484,1649,5698,20055,71373,256998,933458,3418160,

%T 12601291,46739440,174281272,652962532,2456802244,9279423954,

%U 35170693226,133726116806,509926989456,1949634581725,7472405641631,28704432909043,110496066015970

%N G.f. satisfies: A(x) = Sum_{n>=0} x^n * Product_{d|n} A(x^d)^(n/d).

%e G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 45*x^5 + 147*x^6 +...

%e such that, by definition,

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

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

%o for(n=0, 35, print1(a(n), ", "))

%Y Cf. A206301.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Feb 06 2012