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 A334986 #7 Feb 16 2025 08:34:00 %S A334986 1,-1,2,-5,9,53,-1107,12983,-116470,560049,8370713,-346902877, %T A334986 7551856337,-117404648467,913399734614,22560135521007, %U A334986 -1393700803877939,44331044030953865,-979905458659247779,10462396536804802459,367799071887303276422,-30046998012662824941947 %N A334986 a(n) = exp(n) * Sum_{k>=0} (-1)^k * n^(k-1) * k^(n-1) / k!. %H A334986 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a> %F A334986 a(n) = Sum_{k=0..n-1} (-1)^k * Stirling2(n-1,k) * n^(k-1). %F A334986 a(n) = BellPolynomial_(n-1)(-n) / n. %t A334986 Table[Sum[(-1)^k StirlingS2[n - 1, k] n^(k - 1), {k, 0, n - 1}], {n, 1, 22}] %t A334986 Table[BellB[n - 1, -n]/n, {n, 1, 22}] %o A334986 (PARI) a(n)={sum(k=0, n-1, (-1)^k * stirling(n-1,k,2) * n^(k-1))} \\ _Andrew Howroyd_, May 18 2020 %Y A334986 Cf. A030019, A052888, A292866. %K A334986 sign %O A334986 1,3 %A A334986 _Ilya Gutkovskiy_, May 18 2020