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 A334258 #7 Feb 16 2025 08:34:00
%S A334258 1,1,1,-5,-74,-679,-4899,-17289,325837,10627109,199348590,2684041427,
%T A334258 15872610469,-546948563407,-27499774835519,-778467357484561,
%U A334258 -15311413773551790,-125363405319188419,6452292137017871097,436442148982835915339,16494863323310244977581
%N A334258 a(n) = (-1)^n * exp(n) * Sum_{k>=1} (-1)^k * n^(k-1) * k^n / k!.
%H A334258 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>
%F A334258 E.g.f.: series reversion of -log(1 - x) * exp(-x).
%F A334258 a(n) = (n - 1)! * [x^n] exp(n*(1 - exp(-x))).
%F A334258 a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling2(n,k) * n^(k-1).
%F A334258 a(n) = (-1)^n * BellPolynomial_n(-n) / n.
%t A334258 nmax = 21; CoefficientList[InverseSeries[Series[-Log[1 - x] Exp[-x], {x, 0, nmax}], x], x] Range[0, nmax]! // Rest
%t A334258 Table[Sum[(-1)^(n - k) StirlingS2[n, k] n^(k - 1), {k, 1, n}], {n, 1, 21}]
%t A334258 Table[(-1)^n BellB[n, -n]/n, {n, 1, 21}]
%o A334258 (PARI) a(n) = sum(k=1, n, (-1)^(n-k) * stirling(n,k,2) * n^(k-1)); \\ _Michel Marcus_, Apr 20 2020
%Y A334258 Cf. A002741, A052888, A292866.
%K A334258 sign
%O A334258 1,4
%A A334258 _Ilya Gutkovskiy_, Apr 20 2020