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 A351161 #5 Feb 04 2022 11:22:22
%S A351161 0,1,0,1,12,109,900,7309,62280,590185,6402360,78347593,1042633908,
%T A351161 14648616757,214421295132,3266839420021,52041902492496,
%U A351161 870810496011793,15326196662766384,283049655668743249,5460180803581446684,109489002283248831037,2273856664328893182324
%N A351161 G.f. A(x) satisfies: A(x) = x + x^2 * A(x/(1 - 6*x)) / (1 - 6*x).
%C A351161 Shifts 2 places left under 6th-order binomial transform.
%F A351161 a(0) = 0, a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 6^k * a(n-k-2).
%t A351161 nmax = 22; A[_] = 0; Do[A[x_] = x + x^2 A[x/(1 - 6 x)]/(1 - 6 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A351161 a[0] = 0; a[1] = 1; a[n_] := a[n] = Sum[Binomial[n - 2, k] 6^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 22}]
%Y A351161 Cf. A000995, A005012, A351028, A351053, A351057, A351128, A351132, A351152.
%K A351161 nonn
%O A351161 0,5
%A A351161 _Ilya Gutkovskiy_, Feb 03 2022