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 A345234 #8 Jun 19 2021 05:09:59
%S A345234 1,1,1,2,3,5,9,17,31,58,112,218,427,844,1683,3381,6824,13842,28226,
%T A345234 57796,118762,244874,506515,1050688,2185095,4555217,9517423,19926174,
%U A345234 41798031,87833877,184881588,389765182,822901122,1739763655,3682955618,7806103024,16564348106,35187631009
%N A345234 G.f. A(x) satisfies: A(x) = x + x^2 * exp(A(x) - A(-x^2)/2 + A(x^3)/3 - A(-x^4)/4 + ...).
%F A345234 G.f.: x + x^2 * Product_{n>=1} (1 + (-x)^n)^((-1)^n*a(n)).
%F A345234 a(n+2) = (1/n) * Sum_{k=1..n} (-1)^(k+1) * ( Sum_{d|k} (-1)^(k/d+d) * d * a(d) ) * a(n-k+2).
%F A345234 a(n) ~ c * d^n / n^(3/2), where d = 2.21094707842288180828190718521597733363607957468229824761... and c = 0.664585976397397791197984310778764361056468131968... - _Vaclav Kotesovec_, Jun 19 2021
%t A345234 nmax = 38; A[_] = 0; Do[A[x_] = x + x^2 Exp[Sum[(-1)^(k + 1) A[(-1)^(k + 1) x^k]/k, {k, 1, nmax}]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%t A345234 a[1] = a[2] = 1; a[n_] := a[n] = (1/(n - 2)) Sum[(-1)^(k + 1) Sum[(-1)^(k/d + d) d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 38}]
%Y A345234 Cf. A007560, A007562, A049075, A345235.
%K A345234 nonn
%O A345234 1,4
%A A345234 _Ilya Gutkovskiy_, Jun 11 2021