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 A334242 #9 Feb 16 2025 08:34:00
%S A334242 1,2,18,273,5812,159255,5336322,211385076,9663571400,500742188415,
%T A334242 29002424377110,1856728690107027,130194428384173116,
%U A334242 9923500366931329282,816909605562423271178,72231668379957026776065,6827368666949651984215824,686970682778467688690704639
%N A334242 a(n) = exp(-n) * Sum_{k>=0} (k + n)^n * n^k / k!.
%H A334242 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>
%F A334242 a(n) = n! * [x^n] exp(n*(exp(x) + x - 1)).
%F A334242 a(n) = Sum_{k=0..n} binomial(n,k) * BellPolynomial_k(n) * n^(n-k).
%F A334242 a(n) ~ c * exp((r^2/(1-r) - 1)*n) * n^n / (1-r)^n, where r = A333761 = 0.59894186245845296434937... is the root of the equation LambertW(r) = 1-r and c = 0.897950293373062982395233981707095204244165706668136925178217032608352851... - _Vaclav Kotesovec_, Jun 09 2020
%t A334242 Table[n! SeriesCoefficient[Exp[n (Exp[x] + x - 1)], {x, 0, n}], {n, 0, 17}]
%t A334242 Join[{1}, Table[Sum[Binomial[n, k] BellB[k, n] n^(n - k), {k, 0, n}], {n, 1, 17}]]
%Y A334242 Cf. A134980, A242817, A334240, A334241, A334243.
%K A334242 nonn
%O A334242 0,2
%A A334242 _Ilya Gutkovskiy_, Apr 19 2020