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 A361539 #7 Mar 24 2023 09:04:03
%S A361539 3,39,426,4550,50085,577731,7022596,90148860,1222753815,17515226465,
%T A361539 264663151038,4212100028994,70475063838361,1237144088015535,
%U A361539 22735980569119560,436467520716475064,8733235757816095083,181740089309026259565,3925458146197916823970
%N A361539 a(n) = A361540(n, n-2) for n >= 2, a diagonal of triangle A361540.
%C A361539 E.g.f. F(x,y) of triangle A361540 satisfies the following.
%C A361539 (1) F(x,y) = Sum_{n>=0} (F(x,y)^n + y)^n * x^n/n!.
%C A361539 (2) F(x,y) = Sum_{n>=0} F(x,y)^(n^2) * exp(y*x*F(x,y)^n) * x^n/n!.
%C A361539 The diagonal above this one in triangle A361540 has e.g.f. x*exp(x)*exp(x*exp(x)).
%H A361539 Paul D. Hanna, <a href="/A361539/b361539.txt">Table of n, a(n) for n = 2..42</a>
%e A361539 E.g.f. A(x) = 3*x^2/2! + 39*x^3/3! + 426*x^4/4! + 4550*x^5/5! + 50085*x^6/6! + 577731*x^7/7! + 7022596*x^8/8! + 90148860*x^9/9! + 1222753815*x^10/10! + ...
%o A361539 (PARI) /* E.g.f. of triangle A361540 is F(x,y) = Sum_{n>=0} (F(x,y)^n + y)^n * x^n/n! */
%o A361539 {A361540(n,k) = my(A = 1); for(i=1,n, A = sum(m=0, n, (A^m + y +x*O(x^n))^m * x^m/m! )); n!*polcoeff(polcoeff(A, n,x),k,y)}
%o A361539 for(n=2, 20, print1(A361540(n,n-2), ", "))
%Y A361539 Cf. A361540.
%K A361539 nonn
%O A361539 2,1
%A A361539 _Paul D. Hanna_, Mar 20 2023