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 A143567 #13 Nov 28 2023 14:28:21
%S A143567 1,1,1,1,5,21,61,211,1401,8065,37241,240021,1997821,14657501,
%T A143567 105629525,958412911,9201199281,86311594881,871038486001,
%U A143567 9432024424585,106531641929781,1271523772132741,15583607760968941,194983864950339851
%N A143567 E.g.f. satisfies A(x) = exp(x*A(x^3/3!)).
%H A143567 Alois P. Heinz, <a href="/A143567/b143567.txt">Table of n, a(n) for n = 0..100</a>
%F A143567 a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/3)} (3*k+1) * a(k) * a(n-1-3*k) / (6^k * k! * (n-1-3*k)!). - _Seiichi Manyama_, Nov 28 2023
%p A143567 A:= proc(n) option remember; if n<=0 then 1 else unapply (convert (series (exp (x*A(n-3)(x^3/6)), x,n+1), polynom),x) fi end: a:= n-> coeff (A(n)(x), x,n)*n!: seq(a(n), n=0..29);
%t A143567 A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^3/3!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient [A[n][x], x, n]*n!; Table[a[n], {n, 0, 29}] (* _Jean-François Alcover_, Feb 13 2014, after Maple *)
%Y A143567 3rd column of A143565.
%Y A143567 Cf. A367719.
%K A143567 nonn
%O A143567 0,5
%A A143567 _Alois P. Heinz_, Aug 24 2008, Aug 25 2008