A192635 - OEIS

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

%S 1,1,2,5,16,57,234,1045,5103,26791,150492,898497,5676600,37797128,

%T 264348852,1936248546,14814452947,118126621277,979597024690,

%U 8432780717866,75227768490441,694375113431739,6622156995890563,65166502098671053

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

%C Compare to g.f. G(x) of A000081 (number of rooted trees with n nodes), which satisfies: G(x) = exp( Sum_{n>=1} x^n*G(x^n)/n ).

%e G.f.: A(x) =  1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 57*x^5 + 234*x^6 +...

%e The g.f. A(x) satisfies:

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

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

%Y Cf. A191412, A192634, A000081.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 06 2011