%I #2 Mar 30 2012 18:37:16
%S 1,2,130,44739500,4611686018516874838,
%T 8507059173023461595807737228465099196,
%U 17552048611426197782986337964292523732529439672780432120964458900
%N G.f.: A(x) = exp( Sum_{n>=1} 2^(n^3)*x^n/n ).
%C Conjecture: given q and m are nonnegative integers, then
%C exp( Sum_{n>=1} q^(n^m)*x^n/n )
%C is a power series in x with integer coefficients.
%e G.f.: A(x) = 1 + 2*x + 130*x^2 + 44739500*x^3 +...
%e log(A(x)) = 2*x + 2^8*x^2/2 + 2^27*x^3/3 + 2^64*x^4/4 +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, 2^(m^3)*x^m/m)+x*O(x^n)), n)}
%Y Cf. A155200.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Mar 19 2009
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