This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A155207 #8 Jun 15 2025 04:17:30
%S A155207 1,4,136,87904,1074100576,225184288253824,787061981348092400896,
%T A155207 45273238870711805132010916864,42535296046210357883346895894694749696,
%U A155207 649556283428320264374891976653586736162144180224
%N A155207 G.f.: A(x) = exp( Sum_{n>=1} 4^(n^2) * x^n/n ), a power series in x with integer coefficients.
%C A155207 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 A155207 G.f. satisfies: A'(x)/A(x) = 4 + 64*x*A'(16*x)/A(16*x). - _Paul D. Hanna_, Nov 15 2022
%F A155207 a(n) ~ 4^(n^2)/n. - _Vaclav Kotesovec_, Oct 31 2024
%e A155207 G.f.: A(x) = 1 + 4*x + 136*x^2 + 87904*x^3 + 1074100576*x^4 +...
%e A155207 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 A155207 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,4^(m^2)*x^m/m)+x*O(x^n)),n)}
%Y A155207 Cf. A060757, A155208, A155209, A155210, variants: A155200, A155203.
%K A155207 nonn
%O A155207 0,2
%A A155207 _Paul D. Hanna_, Feb 04 2009