cp's OEIS Frontend

A155203 G.f.: A(x) = exp( Sum_{n>=1} 3^(n^2) * x^n/n ), a power series in x with integer coefficients.

%I A155203 #8 Jun 15 2025 04:04:57
%S A155203 1,3,45,6687,10782369,169490304819,25016281429306077,
%T A155203 34185693516532070487615,429210580094546346191627404353,
%U A155203 49269611092414945570325157106493868771
%N A155203 G.f.: A(x) = exp( Sum_{n>=1} 3^(n^2) * x^n/n ), a power series in x with integer coefficients.
%C A155203 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 A155203 Equals column 0 of triangle A155812.
%F A155203 G.f. satisfies: A'(x)/A(x) = 3 + 27*x*A'(9*x)/A(9*x). - _Paul D. Hanna_, Nov 15 2022
%F A155203 a(n) ~ 3^(n^2)/n. - _Vaclav Kotesovec_, Oct 31 2024
%e A155203 G.f.: A(x) = 1 + 3*x + 45*x^2 + 6687*x^3 + 10782369*x^4 + 169490304819*x^5 +...
%e A155203 log(A(x)) = 3*x + 3^4*x^2/2 + 3^9*x^3/3 + 3^16*x^4/4 + 3^25*x^5/5 +...
%o A155203 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,3^(m^2)*x^m/m)+x*O(x^n)),n)}
%Y A155203 Cf. A060722, A155204, A155205, A155206, A155812 (triangle), variants: A155200, A155207.
%K A155203 nonn
%O A155203 0,2
%A A155203 _Paul D. Hanna_, Feb 04 2009