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A155203 G.f.: A(x) = exp( Sum_{n>=1} 3^(n^2) * x^n/n ), a power series in x with integer coefficients. 11

%I

%S 1,3,45,6687,10782369,169490304819,25016281429306077,

%T 34185693516532070487615,429210580094546346191627404353,

%U 49269611092414945570325157106493868771

%N G.f.: A(x) = exp( Sum_{n>=1} 3^(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 Equals column 0 of triangle A155812.

%F G.f. satisfies: A'(x)/A(x) = 3 + 27*x*A'(9*x)/A(9*x). - _Paul D. Hanna_, Nov 15 2022

%e G.f.: A(x) = 1 + 3*x + 45*x^2 + 6687*x^3 + 10782369*x^4 + 169490304819*x^5 +...

%e 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 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,3^(m^2)*x^m/m)+x*O(x^n)),n)}

%Y Cf. A155204, A155205, A155206, A155812 (triangle), variants: A155200, A155207.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 04 2009

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Last modified February 7 10:30 EST 2023. Contains 360115 sequences. (Running on oeis4.)