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%I #4 Nov 15 2022 00:59:02
%S 1,4,136,87904,1074100576,225184288253824,787061981348092400896,
%T 45273238870711805132010916864,42535296046210357883346895894694749696,
%U 649556283428320264374891976653586736162144180224
%N G.f.: A(x) = exp( Sum_{n>=1} 4^(n^2) * x^n/n ), a power series in x with integer coefficients.
%C More generally, for m integer, exp( Sum_{n>=1} m^(n^2) * x^n/n ) is a power series in x with integer coefficients.
%F G.f. satisfies: A'(x)/A(x) = 4 + 64*x*A'(16*x)/A(16*x). - _Paul D. Hanna_, Nov 15 2022
%e G.f.: A(x) = 1 + 4*x + 136*x^2 + 87904*x^3 + 1074100576*x^4 +...
%e log(A(x)) = 4*x + 4^4*x^2/2 + 4^9*x^3/3 + 4^16*x^4/4 + 4^25*x^5/5 +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,4^(m^2)*x^m/m)+x*O(x^n)),n)}
%Y Cf. A155208, A155209, A155210, variants: A155200, A155203.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Feb 04 2009
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