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 A318181 #14 Feb 16 2025 08:33:56
%S A318181 1,1,-5,19,1,-1103,15211,-123821,120865,19464193,-474727877,
%T A318181 7017193075,-50549088671,-931708750607,49742453940331,
%U A318181 -1276858353426317,21239149342811329,-100057086073774463,-9091588769200298501,454849803186974314579,-13529950476868715792063,262961916344710204693681
%N A318181 Expansion of e.g.f. exp((1 - exp(-6*x))/6).
%H A318181 Seiichi Manyama, <a href="/A318181/b318181.txt">Table of n, a(n) for n = 0..447</a>
%H A318181 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>
%F A318181 a(n) = Sum_{k=0..n} (-6)^(n-k)*Stirling2(n,k).
%F A318181 a(0) = 1; a(n) = Sum_{k=1..n} (-6)^(k-1)*binomial(n-1,k-1)*a(n-k).
%F A318181 a(n) = (-6)^n*BellPolynomial_n(-1/6). - _Peter Luschny_, Aug 20 2018
%p A318181 seq(n!*coeff(series(exp((1-exp(-6*x))/6),x=0,22),x,n),n=0..21); # _Paolo P. Lava_, Jan 09 2019
%t A318181 nmax = 21; CoefficientList[Series[Exp[(1 - Exp[-6 x])/6], {x, 0, nmax}], x] Range[0, nmax]!
%t A318181 Table[Sum[(-6)^(n - k) StirlingS2[n, k], {k, 0, n}], {n, 0, 21}]
%t A318181 a[n_] := a[n] = Sum[(-6)^(k - 1) Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 21}]
%t A318181 Table[(-6)^n BellB[n, -1/6], {n, 0, 21}] (* _Peter Luschny_, Aug 20 2018 *)
%Y A318181 Cf. A005012, A008542, A009235, A014182, A317996, A318179, A318180.
%K A318181 sign
%O A318181 0,3
%A A318181 _Ilya Gutkovskiy_, Aug 20 2018