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 A318183 #15 Feb 16 2025 08:33:56
%S A318183 1,1,-1,1,25,-674,15211,-331827,5987745,15901597,-13125035449,
%T A318183 1292056076070,-103145930581319,7462324963409941,-464957409070517453,
%U A318183 16313974895147212801,2059903411953959582849,-708700955022151333496910,143215213612865558214820303,-24681846509158429152517973103
%N A318183 a(n) = [x^n] Sum_{k>=0} x^k/Product_{j=1..k} (1 + n*j*x).
%H A318183 Seiichi Manyama, <a href="/A318183/b318183.txt">Table of n, a(n) for n = 0..282</a>
%H A318183 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>
%F A318183 a(n) = n! * [x^n] exp((1 - exp(-n*x))/n), for n > 0.
%F A318183 a(n) = Sum_{k=0..n} (-n)^(n-k)*Stirling2(n,k).
%F A318183 a(n) = (-n)^n*BellPolynomial_n(-1/n) for n >= 1. - _Peter Luschny_, Aug 20 2018
%t A318183 Table[SeriesCoefficient[Sum[x^k/Product[(1 + n j x), {j, 1, k}], {k, 0, n}], {x, 0, n}], {n, 0, 19}]
%t A318183 Join[{1}, Table[n! SeriesCoefficient[Exp[(1 - Exp[-n x])/n], {x, 0, n}], {n, 19}]]
%t A318183 Join[{1}, Table[Sum[(-n)^(n - k) StirlingS2[n, k], {k, n}], {n, 19}]]
%t A318183 Join[{1}, Table[(-n)^n BellB[n, -1/n], {n, 1, 21}]] (* _Peter Luschny_, Aug 20 2018 *)
%o A318183 (PARI) {a(n) = sum(k=0, n, (-n)^(n-k)*stirling(n, k, 2))} \\ _Seiichi Manyama_, Jul 27 2019
%Y A318183 Cf. A009235, A014182, A292866, A301419, A317996, A318179, A318180, A318181.
%K A318183 sign
%O A318183 0,5
%A A318183 _Ilya Gutkovskiy_, Aug 20 2018