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 A360193 #38 Feb 16 2025 08:34:04
%S A360193 -1,0,2,9,52,445,5166,75019,1300776,26167257,598577770,15337224991,
%T A360193 435020120316,13529095809541,457727913937854,16736043791509995,
%U A360193 657590281425958096,27631245762003186865,1236355641557737359570,58689534518861119967287
%N A360193 a(n) = Sum_{k=0..n} (k-1)^(k-1) * binomial(n,k).
%H A360193 Winston de Greef, <a href="/A360193/b360193.txt">Table of n, a(n) for n = 0..385</a>
%H A360193 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A360193 E.g.f.: -exp(x + LambertW(-x)).
%F A360193 E.g.f.: x * exp(x) / LambertW(-x).
%F A360193 a(n) ~ exp(exp(-1)-1) * n^(n-1). - _Vaclav Kotesovec_, Mar 06 2023
%o A360193 (PARI) a(n) = sum(k=0, n, (k-1)^(k-1)*binomial(n, k));
%o A360193 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x+lambertw(-x))))
%o A360193 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(x*exp(x)/lambertw(-x)))
%Y A360193 Cf. A088957, A105785, A177885, A277473.
%K A360193 sign,easy
%O A360193 0,3
%A A360193 _Seiichi Manyama_, Mar 05 2023