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 A352044 #10 May 30 2022 09:55:01
%S A352044 1,1,1,2,4,8,16,33,71,159,367,864,2058,4934,11870,28608,69020,166652,
%T A352044 402748,974464,2361416,5733656,13954488,34054016,83351472,204659440,
%U A352044 504162416,1246065920,3089752480,7685498976,19174255584,47971104769,120326714335
%N A352044 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * a(k).
%H A352044 Seiichi Manyama, <a href="/A352044/b352044.txt">Table of n, a(n) for n = 0..1000</a>
%F A352044 G.f. A(x) satisfies: A(x) = 1 + x * A(x^2/(1 - x)^2) / (1 - x).
%F A352044 E.g.f.: Integral exp(x) * Sum_{n>=0} a(n) * x^(2*n) / (2*n)! dx.
%t A352044 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 2 k] a[k], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 32}]
%t A352044 nmax = 32; A[_] = 0; Do[A[x_] = 1 + x A[x^2/(1 - x)^2]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A352044 Cf. A027826, A352045, A352066.
%K A352044 nonn
%O A352044 0,4
%A A352044 _Ilya Gutkovskiy_, Mar 01 2022