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 A351053 #12 Feb 04 2022 11:23:23
%S A351053 0,1,0,1,6,28,126,613,3438,22159,157362,1189126,9436320,78690781,
%T A351053 692478684,6439539457,63106488618,648453907216,6952719052134,
%U A351053 77521908188737,897132401326458,10764085132255807,133774484448519294,1720018195807299418,22847325911461934352
%N A351053 G.f. A(x) satisfies: A(x) = x + x^2 * A(x/(1 - 3*x)) / (1 - 3*x).
%C A351053 Shifts 2 places left under 3rd-order binomial transform.
%F A351053 a(0) = 0, a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 3^k * a(n-k-2).
%t A351053 nmax = 24; A[_] = 0; Do[A[x_] = x + x^2 A[x/(1 - 3 x)]/(1 - 3 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A351053 a[0] = 0; a[1] = 1; a[n_] := a[n] = Sum[Binomial[n - 2, k] 3^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 24}]
%Y A351053 Cf. A000995, A004212, A351028, A351049, A351128, A351132, A351144, A351161.
%K A351053 nonn
%O A351053 0,5
%A A351053 _Ilya Gutkovskiy_, Feb 03 2022