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G.f.: A(x) = x*exp( Sum_{n>=1} A(2^(n^2)*x^n)/n ).
1

%I #2 Mar 30 2012 18:37:23

%S 1,2,18,348,22998,7497180,11948631604,81974855239480,

%T 2326992693663022694,269846257532329078280364,

%U 127041922315653022761148802396,241938253359964848636177506896485640

%N G.f.: A(x) = x*exp( Sum_{n>=1} A(2^(n^2)*x^n)/n ).

%C Compare g.f. to that of A000081 (number of rooted trees with n nodes):

%C * G(x) = x*exp( Sum_{n>=1} G(x^n)/n ).

%e G.f.: A(x) = 1 + 2*x + 18*x^2 + 348*x^3 + 22998*x^4 + 7497180*x^5 +...

%e A(x) = x*exp(A(2*x) + A(2^4*x^2)/2 + A(2^9*x^3)/3 + A(2^16*x^4)/4 +...).

%o (PARI) {a(n)=local(A=x+2*x^2);for(i=1,n,A=x*exp(sum(m=1,n,subst(A,x,2^(m^2)*x^m+x*O(x^n))/m)));polcoeff(A,n)}

%Y Cf. A181535.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Oct 30 2010