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 A346771 #9 Feb 23 2022 07:31:10
%S A346771 1,1,1,3,7,23,81,325,1429,6851,35443,196507,1160633,7266561,48022313,
%T A346771 333776331,2432140759,18528143535,147201596073,1216952016245,
%U A346771 10448532393869,92999784076875,856739848236627,8156691628658019,80147320081510673,811770418508099905
%N A346771 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)) / (1 - x^2).
%H A346771 Seiichi Manyama, <a href="/A346771/b346771.txt">Table of n, a(n) for n = 0..577</a>
%F A346771 E.g.f.: exp(-x) * (2 * exp(exp(x) - 1) - 1).
%F A346771 a(0) = a(1) = 1; a(n) = Sum_{k=1..n-1} binomial(n-1,k) * a(n-k-1).
%F A346771 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A186021(k).
%F A346771 a(n) = 2 * A000296(n) - (-1)^n.
%t A346771 nmax = 25; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - x)]/(1 - x^2) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A346771 nmax = 25; CoefficientList[Series[Exp[-x] (2 Exp[Exp[x] - 1] - 1), {x, 0, nmax}], x] Range[0, nmax]!
%t A346771 a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k] a[n - k - 1], {k, 1, n - 1}]; Table[a[n], {n, 0, 25}]
%Y A346771 Cf. A000110, A000296, A040027, A060719, A186021, A344489.
%K A346771 nonn
%O A346771 0,4
%A A346771 _Ilya Gutkovskiy_, Aug 02 2021