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 A344489 #5 May 21 2021 08:07:20
%S A344489 1,1,2,4,11,34,122,487,2144,10276,53165,294760,1740950,10899841,
%T A344489 72033470,500664496,3648211139,27792215302,220802394110,1825428024367,
%U A344489 15672798590804,139499676115312,1285109772354941,12235037442987028,120220980122266010,1217655627762149857
%N A344489 a(n) = 1 + Sum_{k=0..n-2} binomial(n-1,k) * a(k).
%F A344489 G.f. A(x) satisfies: A(x) = (1 + x * A(x/(1 - x))) / (1 - x^2).
%t A344489 a[n_] := a[n] = 1 + Sum[Binomial[n - 1, k] a[k] , {k, 0, n - 2}]; Table[a[n], {n, 0, 25}]
%t A344489 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]
%Y A344489 Cf. A000296, A000629, A007476, A186021, A337186, A344490, A344491, A344492, A344493.
%K A344489 nonn
%O A344489 0,3
%A A344489 _Ilya Gutkovskiy_, May 21 2021