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 A351151 #6 Feb 03 2022 09:42:27
%S A351151 1,0,1,5,26,145,901,6420,52501,480955,4795626,51066375,576182001,
%T A351151 6879462680,86955722401,1162559359745,16392133866026,242734091500445,
%U A351151 3758825675820501,60660434188558780,1017770666417312501,17725289455315892375,320047193447632729626
%N A351151 G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 5*x)) / (1 - 5*x).
%C A351151 Shifts 2 places left under 5th-order binomial transform.
%F A351151 a(0) = 1, a(1) = 0; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 5^k * a(n-k-2).
%t A351151 nmax = 22; A[_] = 0; Do[A[x_] = 1 + x^2 A[x/(1 - 5 x)]/(1 - 5 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A351151 a[0] = 1; a[1] = 0; a[n_] := a[n] = Sum[Binomial[n - 2, k] 5^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 22}]
%Y A351151 Cf. A000994, A005011, A351056, A351143, A351144, A351150, A351152.
%K A351151 nonn
%O A351151 0,4
%A A351151 _Ilya Gutkovskiy_, Feb 02 2022