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 A307605 #9 Mar 19 2021 11:53:39
%S A307605 1,1,2,5,12,20,48,81,169,305,580,1009,1966,3338,6067,10503,18730,
%T A307605 31633,55641,93151,160389,267585,452762,747016,1253644,2049943,
%U A307605 3390786,5516227,9034745,14572790,23668066,37918484,61042425,97231826,155292944,245774727,389998116
%N A307605 G.f. A(x) satisfies: A(x) = (1 + x) * A(x^2)^2*A(x^3)^3*A(x^4)^4* ... *A(x^k)^k* ...
%C A307605 Weigh transform of A050369.
%H A307605 Vaclav Kotesovec, <a href="/A307605/b307605.txt">Table of n, a(n) for n = 0..5000</a>
%F A307605 G.f.: Product_{k>=1} (1 + x^k)^(k*A074206(k)).
%F A307605 a(n) ~ ((2^(-1-r) - 1) * Gamma(2+r) * zeta(2+r) / zeta'(r))^(1/(4 + 2*r)) * exp((2+r)/(1+r) * ((2^(-1-r) - 1) * Gamma(2+r) * zeta(2+r) / zeta'(r))^(1/(2+r)) * n^((1+r)/(2+r))) / (2^(1/50) * sqrt(Pi*(2+r)) * n^((3 + r)/(4 + 2*r))), where r = A107311 is the root of the equation zeta(r) = 2. - _Vaclav Kotesovec_, Mar 18 2021
%e A307605 G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 12*x^4 + 20*x^5 + 48*x^6 + 81*x^7 + 169*x^8 + 305*x^9 + ...
%t A307605 terms = 36; A[_] = 1; Do[A[x_] = (1 + x) Product[A[x^k]^k, {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
%Y A307605 Cf. A050369, A074206, A129373, A307604, A307606.
%K A307605 nonn
%O A307605 0,3
%A A307605 _Ilya Gutkovskiy_, Apr 18 2019