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 A335849 #4 Jun 26 2020 23:44:52
%S A335849 1,1,3,14,87,675,6282,68201,846183,11811048,183176577,3124958179,
%T A335849 58157682072,1172551946395,25459025908899,592263131497942,
%U A335849 14696581853565723,387477880784385143,10816856730117090114,318739828787430822853,9886623306152849028771
%N A335849 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * Bell(k-1) * a(n-k).
%F A335849 E.g.f.: exp(1) / (exp(1) + Ei(1) - Ei(exp(x))), where Ei() is the exponential integral.
%t A335849 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] BellB[k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
%t A335849 nmax = 20; CoefficientList[Series[Exp[1]/(Exp[1] + ExpIntegralEi[1] - ExpIntegralEi[Exp[x]]), {x, 0, nmax}], x] Range[0, nmax]!
%Y A335849 Cf. A000110, A004122, A083355, A129247, A137551.
%K A335849 nonn
%O A335849 0,3
%A A335849 _Ilya Gutkovskiy_, Jun 26 2020