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 A362862 #13 Aug 07 2025 06:14:09
%S A362862 1,0,13,629,58993,8998399,2035844461,640881617123,267995012680641,
%T A362862 143734541641235567,96200314049944377901,78599287990433271805699,
%U A362862 76993408916168689318057201,89072357257840197226050646151
%N A362862 a(n) = (-1)^n * Sum_{k=0..n} (-n*k)^k * binomial(n,k).
%H A362862 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362862 a(n) = n! * [x^n] exp(-x) / (1 + LambertW(-n*x)).
%F A362862 a(n) = [x^n] Sum_{k>=0} (n*k*x)^k / (1 + x)^(k+1).
%t A362862 Table[(-1)^n*(1 + Sum[(-n*k)^k*Binomial[n, k], {k, 1, n}]), {n, 0, 20}] (* _Vaclav Kotesovec_, Aug 07 2025 *)
%o A362862 (PARI) a(n) = (-1)^n * sum(k=0, n, (-n*k)^k*binomial(n, k));
%Y A362862 Main diagonal of A362019.
%Y A362862 Cf. A290158.
%K A362862 nonn
%O A362862 0,3
%A A362862 _Seiichi Manyama_, May 06 2023