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 A335441 #7 Jun 11 2020 09:09:40
%S A335441 1,1,2,4,11,40,176,907,5360,35668,263789,2146390,19054040,183248581,
%T A335441 1897952690,21061861828,249309196559,3135518918800,41754612283244,
%U A335441 586922460056851,8684272948653068,134919751191875572,2195942678525060093,37365571515146318650
%N A335441 a(n) = 1 + Sum_{k=1..n-1} binomial(n-2,k-1) * a(k) * a(n-k-1).
%H A335441 Vaclav Kotesovec, <a href="/A335441/b335441.txt">Table of n, a(n) for n = 0..470</a>
%F A335441 E.g.f. A(x) satisfies: A''(x) = exp(x) + A(x) * A'(x).
%F A335441 From _Vaclav Kotesovec_, Jun 11 2020: (Start)
%F A335441 E.g.f.: (BesselY(0, sqrt(2))*(BesselJ(1, sqrt(2)*exp(x/2)) - sqrt(2)*exp(x/2)*BesselJ(0, sqrt(2)*exp(x/2))) + BesselJ(0, sqrt(2))*(sqrt(2)*exp(x/2)*BesselY(0, sqrt(2)*exp(x/2)) - BesselY(1, sqrt(2)*exp(x/2)))) / (BesselJ(1, sqrt(2)*exp(x/2))*BesselY(0, sqrt(2)) - BesselJ(0, sqrt(2))*BesselY(1, sqrt(2)*exp(x/2))).
%F A335441 a(n) ~ 2 * n! / r^(n+1), where r = 1.35169030867903432729790416904526340210784862703704233748118252928787... is the smallest real root of the equation BesselY(0, sqrt(2))*BesselJ(1, sqrt(2)*exp(r/2)) = BesselJ(0, sqrt(2))*BesselY(1, sqrt(2)*exp(r/2)). (End)
%t A335441 a[n_] := a[n] = 1 + Sum[Binomial[n - 2, k - 1] a[k] a[n - k - 1], {k, 1, n - 1}]; Table[a[n], {n, 0, 23}]
%t A335441 terms = 23; A[_] = 0; Do[A[x_] = Normal[Integrate[Integrate[Exp[x] + A[x] D[A[x], x], x], x] + O[x]^(terms + 1)], terms]; CoefficientList[A[x], x] Range[0, terms]!
%Y A335441 Cf. A000111, A006677, A052886, A054687, A080635, A332776.
%K A335441 nonn
%O A335441 0,3
%A A335441 _Ilya Gutkovskiy_, Jun 10 2020