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 A351810 #6 Feb 20 2022 06:46:04
%S A351810 1,1,9,69,565,5305,56929,680685,8902349,126121313,1923133433,
%T A351810 31379181461,544931376229,10024917092105,194602995875985,
%U A351810 3972686705253181,85035210652191485,1903471938128641457,44453001710603619369,1080789854059236415973,27304602412815047204501
%N A351810 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 4*x)) / (1 - 4*x)^2.
%F A351810 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k-1) * 4^(k-1) * a(n-k).
%t A351810 nmax = 20; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - 4 x)]/(1 - 4 x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
%t A351810 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 4^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
%Y A351810 Cf. A004213, A040027, A326324, A351756, A351757, A351811, A351812.
%K A351810 nonn
%O A351810 0,3
%A A351810 _Ilya Gutkovskiy_, Feb 19 2022