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 A351128 #34 Feb 04 2022 11:23:42
%S A351128 0,1,0,1,8,49,280,1649,10800,81505,696400,6472033,63562872,652984977,
%T A351128 7026210728,79547049681,949709767904,11936248012993,157219119485216,
%U A351128 2159448120457409,30811324011852136,455635009201780977,6975424580445456056,110478282815356437809
%N A351128 G.f. A(x) satisfies: A(x) = x + x^2 * A(x/(1 - 4*x)) / (1 - 4*x).
%C A351128 Shifts 2 places left under 4th-order binomial transform.
%F A351128 a(0) = 0, a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 4^k * a(n-k-2).
%t A351128 nmax = 23; A[_] = 0; Do[A[x_] = x + x^2 A[x/(1 - 4 x)]/(1 - 4 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A351128 a[0] = 0; a[1] = 1; a[n_] := a[n] = Sum[Binomial[n - 2, k] 4^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 23}]
%Y A351128 Cf. A000995, A004213, A351028, A351050, A351053, A351132, A351150, A351161.
%K A351128 nonn
%O A351128 0,5
%A A351128 _Ilya Gutkovskiy_, Feb 03 2022