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 A354736 #7 Jun 06 2022 02:51:55
%S A354736 1,1,5,10,55,150,775,2550,12500,46250,219375,875000,4075000,17071250,
%T A354736 78796875,341100000,1569350000,6947531250,31966000000,143761750000,
%U A354736 662668906250,3014440000000,13932834296875,63921914062500,296358191406250,1368603488281250,6365085546875000
%N A354736 a(0) = a(1) = 1; a(n) = 5 * Sum_{k=0..n-2} a(k) * a(n-k-2).
%F A354736 G.f. A(x) satisfies: A(x) = 1 + x + 5 * (x * A(x))^2.
%F A354736 G.f.: (1 - sqrt(1 - 20 * x^2 * (1 + x))) / (10 * x^2).
%F A354736 a(n) ~ sqrt((2+3*r)*(1+r)) / (sqrt(Pi) * n^(3/2) * r^n), where r = 2*cos(arccos(-13/40)/3)/3 - 1/3. - _Vaclav Kotesovec_, Jun 04 2022
%t A354736 a[0] = a[1] = 1; a[n_] := a[n] = 5 Sum[a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]
%t A354736 nmax = 26; CoefficientList[Series[(1 - Sqrt[1 - 20 x^2 (1 + x)])/(10 x^2), {x, 0, nmax}], x]
%Y A354736 Cf. A007477, A156058, A354733, A354734, A354735.
%K A354736 nonn
%O A354736 0,3
%A A354736 _Ilya Gutkovskiy_, Jun 04 2022