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 A334240 #13 Feb 16 2025 08:34:00
%S A334240 1,2,11,103,1357,23031,478207,11741094,332734521,10689163687,
%T A334240 383851610331,15236978883127,662491755803269,31311446539427926,
%U A334240 1598351161031967063,87638233726766111731,5136809177699534717169,320521818480481139673919,21212211430440994022892019
%N A334240 a(n) = exp(-n) * Sum_{k>=0} (k + 1)^n * n^k / k!.
%H A334240 Seiichi Manyama, <a href="/A334240/b334240.txt">Table of n, a(n) for n = 0..368</a>
%H A334240 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>
%F A334240 a(n) = [x^n] (1/(1 - x)) * Sum_{k>=0} (n*x/(1 - x))^k / Product_{j=1..k} (1 - j*x/(1 - x)).
%F A334240 a(n) = n! * [x^n] exp(x + n*(exp(x) - 1)).
%F A334240 a(n) = Sum_{k=0..n} binomial(n,k) * BellPolynomial_k(n).
%F A334240 a(n) ~ exp((1/LambertW(1) - 2)*n) * n^n / (sqrt(1+LambertW(1)) * LambertW(1)^(n+1)). - _Vaclav Kotesovec_, Jun 08 2020
%t A334240 Table[n! SeriesCoefficient[Exp[x + n (Exp[x] - 1)], {x, 0, n}], {n, 0, 18}]
%t A334240 Table[Sum[Binomial[n, k] BellB[k, n], {k, 0, n}], {n, 0, 18}]
%Y A334240 Cf. A242817, A299824, A334162, A334241, A334242, A334243.
%K A334240 nonn
%O A334240 0,2
%A A334240 _Ilya Gutkovskiy_, Apr 19 2020