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 A334241 #6 Feb 16 2025 08:34:00
%S A334241 1,0,-1,7,-43,221,-341,-15980,370761,-5688125,62689871,-197586839,
%T A334241 -14973562979,585250669316,-14306382821485,240985102271971,
%U A334241 -1121421968408303,-122020498882279931,6674724196051810807,-223424819176020519168,5051515662105879438501
%N A334241 a(n) = exp(n) * Sum_{k>=0} (k + 1)^n * (-n)^k / k!.
%H A334241 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>
%F A334241 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 A334241 a(n) = n! * [x^n] exp(x + n*(1 - exp(x))).
%F A334241 a(n) = Sum_{k=0..n} binomial(n,k) * BellPolynomial_k(-n).
%t A334241 Table[n! SeriesCoefficient[Exp[x + n (1 - Exp[x])], {x, 0, n}], {n, 0, 20}]
%t A334241 Table[Sum[Binomial[n, k] BellB[k, -n], {k, 0, n}], {n, 0, 20}]
%Y A334241 Cf. A292866, A334193, A334240, A334242, A334243.
%K A334241 sign
%O A334241 0,4
%A A334241 _Ilya Gutkovskiy_, Apr 19 2020