A198413 - OEIS

%I #11 Mar 30 2012 18:37:31

%S 1,1,3,11,46,205,962,4668,23268,118374,612305,3210348,17023682,

%T 91140496,491968036,2674572509,14631157562,80480706331,444865534251,

%U 2469826058736,13766223517639,77003660186990,432131032213098,2432230966070833,13726899289265314

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

%e G.f.: A(x) = 1 + x + 3*x^2 + 11*x^3 + 46*x^4 + 205*x^5 + 962*x^6 +...

%e where

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

%e more explicitly,

%e log(A(x)) = x + 5*x^2/2 + 25*x^3/3 + 133*x^4/4 + 716*x^5/5 + 3947*x^6/6 +...

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

%Y Cf. A198520.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 26 2011