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 A361688 #6 Mar 24 2023 09:03:54
%S A361688 1,2,71,10915,4063645,2842101221,3255178907803,5605980824208871,
%T A361688 13710496284516264953,45746570903514799640905,
%U A361688 202291094041887013214628871,1160411497892246920315488823067,8496377826955803443098054623140629,78398366060939693412478828210386035725
%N A361688 a(n) = A361540(2*n,n) / binomial(2*n,n) for n >= 0.
%C A361688 E.g.f. F(x,y) of triangle A361540 satisfies the following.
%C A361688 (1) F(x,y) = Sum_{n>=0} (F(x,y)^n + y)^n * x^n/n!.
%C A361688 (2) F(x,y) = Sum_{n>=0} F(x,y)^(n^2) * exp(y*x*F(x,y)^n) * x^n/n!.
%C A361688 This sequence equals the central terms of triangle A361540 divided by the central binomial coefficients A000984.
%H A361688 Paul D. Hanna, <a href="/A361688/b361688.txt">Table of n, a(n) for n = 0..25</a>
%e A361688 E.g.f. A(x) = 1 + 2*x + 71*x^2/2! + 10915*x^3/3! + 4063645*x^4/4! + 2842101221*x^5/5! + 3255178907803*x^6/6! + 5605980824208871*x^7/7! + 13710496284516264953*x^8/8! + ... + a(n)*x^n/n! + ...
%o A361688 (PARI) /* E.g.f. of triangle A361540 is F(x,y) = Sum_{n>=0} (F(x,y)^n + y)^n * x^n/n! */
%o A361688 {A361540(n,k) = my(F = 1); for(i=1,n, F = sum(m=0, n, (F^m + y +x*O(x^n))^m * x^m/m! )); n!*polcoeff(polcoeff(F, n,x),k,y)}
%o A361688 {a(n) = A361540(2*n,n)/binomial(2*n,n)}
%o A361688 for(n=0, 15, print1(a(n), ", "))
%Y A361688 Cf. A361540, A000984.
%K A361688 nonn
%O A361688 0,2
%A A361688 _Paul D. Hanna_, Mar 20 2023