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 A086914 #15 Jun 06 2022 11:19:01
%S A086914 0,3,11,95,1414,31619,980328,39966975,2063473712,131165658459,
%T A086914 10041515879680,909567637557215,96070344004816128,
%U A086914 11688399779985830355,1621144844290431509504,254042974238965752088575
%N A086914 a(n) = ((n-1)^n/n)*Sum_{k>=1} (k^n/n^k).
%C A086914 Appears to always be an integer.
%F A086914 a(n) = Euler(n, n)/(n-1) where Euler(n, x) is Eulerian polynomial of degree n (cf. A008292). - _Vladeta Jovovic_, Sep 26 2003
%F A086914 a(n) = (n-1)^n/n*polylog(-n, 1/n) = 1/(n-1)*Sum(n^i*Sum((-1)^j*binomial(n+1, j)*(i-j+1)^n, j = 0 .. i), i = 0 .. n), n>1. - _Vladeta Jovovic_, Sep 26 2003
%F A086914 Prime p divides a(p-1) for p>2. - _Alexander Adamchuk_, Sep 19 2006
%F A086914 a(n) = A122020[n] / (n*(n-1)) for n>1. a(n) = A122778[n] / (n-1) for n>1. a(n) = ((n-1)^n)/n * A121376[n]/A121985[n] for n>1. - _Alexander Adamchuk_, Sep 19 2006
%F A086914 a(n) ~ exp(-1) * n! * n^(n-1) / log(n)^(n+1). - _Vaclav Kotesovec_, Jun 06 2022
%t A086914 Table[Sum[(n-1)^n*k^n/n^(k+1), {k, 1, Infinity}], {n, 1, 20}] (* _Vaclav Kotesovec_, Oct 16 2016 *)
%Y A086914 Cf. A122020, A122778, A121376, A121985.
%K A086914 nonn
%O A086914 1,2
%A A086914 _Benoit Cloitre_, Sep 24 2003