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 A334243 #5 Feb 16 2025 08:34:00
%S A334243 1,0,-2,-3,44,245,-2346,-33278,186808,6888555,-6774910,-1986368439,
%T A334243 -10227075420,738830661296,10363304656782,-327255834908715,
%U A334243 -9380517430358288,152180429032236325,9132761207739810618,-46897839494116200918,-9833058047657527541220
%N A334243 a(n) = exp(n) * Sum_{k>=0} (k + n)^n * (-n)^k / k!.
%H A334243 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>
%F A334243 a(n) = n! * [x^n] exp(n*(1 + x - exp(x))).
%F A334243 a(n) = Sum_{k=0..n} binomial(n,k) * BellPolynomial_k(-n) * n^(n-k).
%t A334243 Table[n! SeriesCoefficient[Exp[n (1 + x - Exp[x])], {x, 0, n}], {n, 0, 20}]
%t A334243 Join[{1}, Table[Sum[Binomial[n, k] BellB[k, -n] n^(n - k), {k, 0, n}], {n, 1, 20}]]
%Y A334243 Cf. A292866, A298373, A334240, A334241, A334242.
%K A334243 sign
%O A334243 0,3
%A A334243 _Ilya Gutkovskiy_, Apr 19 2020