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 A155209 #4 Jun 15 2025 04:21:41
%S A155209 1,3,117,83691,1057319541,224085796087563,785909534807110163445,
%T A155209 45253898808490419883694669835,42530103981310660908750359650219091445,
%U A155209 649533982980850199063905669772208004250784346635
%N A155209 G.f.: A(x) = exp( Sum_{n>=1} (4^n - 1)^n * x^n/n ), a power series in x with integer coefficients.
%C A155209 More generally, for m integer, exp( Sum_{n>=1} (m^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.
%e A155209 G.f.: A(x) = 1 + 3*x + 117*x^2 + 83691*x^3 + 1057319541*x^4 +...
%e A155209 log(A(x)) = 3*x + 15^2*x^2/2 + 63^3*x^3/3 + 255^4*x^4/4 + 1023^5*x^5/5 +...
%o A155209 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,(4^m-1)^m*x^m/m)+x*O(x^n)),n)}
%Y A155209 Cf. A155207, A155208, A155210, A241098; variants: A155202, A155205.
%K A155209 nonn
%O A155209 0,2
%A A155209 _Paul D. Hanna_, Feb 04 2009