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G.f.: A(x) = exp( Sum_{n>=1} A(2^(n^2)*x^n)*x^n/n ).
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%I #2 Mar 30 2012 18:37:23

%S 1,1,3,15,145,2489,83021,5402565,697174827,179186086779,

%T 91923934089991,94222398574777359,193061880430280639843,

%U 790974713509247761511635,6480456214858268755580705051,106182276664343738404944887223883

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

%e G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 145*x^4 + 2489*x^5 +...

%e The logarithm of the g.f. equals the series:

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

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

%Y Cf. A181536.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 30 2010