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 A347953 #28 Jul 20 2023 15:15:03
%S A347953 1,1,2,8,35,171,882,4744,26286,149045,860596,5042968,29913676,
%T A347953 179270434,1083794310,6601817952,40479778395,249646876065,
%U A347953 1547539929810,9637085582640,60260786147261,378212395786511,2381767469829332,15045137488662048,95304451461770250
%N A347953 G.f.: A(x) = 1/C(-x*T(x)^3), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108 and T(x) = 1 + x*T(x)^3 is the g.f. of A001764.
%H A347953 Alexander Burstein and Louis W. Shapiro, <a href="https://arxiv.org/abs/2112.11595">Pseudo-involutions in the Riordan group</a>, arXiv:2112.11595 [math.CO], 2021.
%F A347953 G.f.: A(-x*A(x)^3) = 1/A(x).
%F A347953 G.f.: The series reversion of x*A(x)^3 is x*A(-x)^3.
%F A347953 G.f.: A(x) satisfies A(x) = 1 + x*(1 - A(x) + A(x)^2)^3/A(x).
%F A347953 D-finite with recurrence +4*n*(4*n-1)*(4*n+1)*a(n) +6*(-342*n^3+1233*n^2-1453*n+542)*a(n-1) +243*(n-2)*(33*n^2-123*n+112)*a(n-2) +2187*(n-3)*(3*n-4)*(3*n-8)*a(n-3)=0. - _R. J. Mathar_, Jul 20 2023
%p A347953 cx := (1-sqrt(1-4*x))/2/x ;
%p A347953 tx := 2/sqrt(3*x)*sin( 1/3*arcsin(sqrt(27*x/4))) ;
%p A347953 gf := 1/subs(x=-x*tx^3,cx) ;
%p A347953 taylor(%,x=0,40) ;
%p A347953 gfun[seriestolist](%) ; # _R. J. Mathar_, Jul 20 2023
%t A347953 CoefficientList[y/.AsymptoticSolve[y-1-x(1-y+y^2)^3/y==0,y->1,{x,0,24}][[1]],x]
%o A347953 (PARI) seq(n) = {Vec(1/subst((1 - sqrt(1 - 4*x + O(x^2*x^n))) / (2*x), x, -serreverse(x / (1+x)^3 + O(x*x^n))))} \\ _Andrew Howroyd_, Nov 22 2021
%Y A347953 Cf. A000108, A001764, A166135.
%K A347953 nonn
%O A347953 0,3
%A A347953 _Alexander Burstein_, Nov 02 2021