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 A335868 #8 Feb 16 2025 08:34:00
%S A335868 1,-2,7,-31,149,-631,475,43210,-844727,10960505,-86569889,-584746911,
%T A335868 46302579229,-1304510879686,25366896568707,-277053418780891,
%U A335868 -4271166460501743,384590020131637825,-14617527176248527545,380117694164438489422,-5265650620303861935579
%N A335868 a(n) = exp(n) * Sum_{k>=0} (-n)^k * (k - 1)^n / k!.
%H A335868 Seiichi Manyama, <a href="/A335868/b335868.txt">Table of n, a(n) for n = 0..200</a>
%H A335868 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>
%F A335868 a(n) = n! * [x^n] exp(n*(1 - exp(x)) - x).
%F A335868 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * BellPolynomial_k(-n).
%t A335868 Table[n! SeriesCoefficient[Exp[n (1 - Exp[x]) - x], {x, 0, n}], {n, 0, 20}]
%t A335868 Table[Sum[(-1)^(n - k) Binomial[n, k] BellB[k, -n], {k, 0, n}], {n, 0, 20}]
%Y A335868 Cf. A109747, A292866, A334241, A335867.
%K A335868 sign
%O A335868 0,2
%A A335868 _Ilya Gutkovskiy_, Jun 27 2020