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 A351969 #5 Feb 28 2022 07:51:54
%S A351969 1,1,1,1,1,2,7,22,57,128,389,1904,9329,38040,132147,542648,3283633,
%T A351969 20997824,114657097,536178880,2784500161,19876061313,153326461333,
%U A351969 1034551840125,6051063487505,38079448058864,312420426286609,2785055245002944,22141255546319849
%N A351969 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-1,4*k) * a(k) * a(n-4*k-1).
%F A351969 E.g.f.: exp( Sum_{n>=0} a(n) * x^(4*n+1) / (4*n+1)! ).
%t A351969 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 4 k] a[k] a[n - 4 k - 1], {k, 0, Floor[(n - 1)/4]}]; Table[a[n], {n, 0, 28}]
%Y A351969 Cf. A138314, A351968.
%K A351969 nonn
%O A351969 0,6
%A A351969 _Ilya Gutkovskiy_, Feb 26 2022