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 A081216 #31 Aug 23 2024 21:08:54
%S A081216 0,1,1,7,51,521,6665,102943,1864135,38742049,909090909,23775972551,
%T A081216 685853880635,21633936185161,740800455037201,27368368148803711,
%U A081216 1085102592571150095,45957792327018709121,2070863582910344082917,98920982783015679456199
%N A081216 a(n) = (n^n-(-1)^n)/(n+1).
%C A081216 a(n) is prime for n = {3, 5, 17, 157} = A056826(n) Primes p such that (p^p + 1)/(p + 1) is a prime. Prime a(n) are {7, 521, 45957792327018709121, ...}. Bisection of a(n) is Sierpinski quotient a(2n-1) = A124899(n) = ((2n-1)^(2n-1) + 1)/(2n) = A014566(2n-1)/(2n). - _Alexander Adamchuk_, Nov 12 2006
%C A081216 This is related to the dimension of the primitive middle cohomology of Dwork hypersurfaces x1**n+x2**n+...+xn**n=n*psi*x1*x2*...*xn. [_F. Chapoton_, Dec 11 2009]
%H A081216 Seiichi Manyama, <a href="/A081216/b081216.txt">Table of n, a(n) for n = 0..387</a>
%H A081216 Philippe Goutet, <a href="https://arxiv.org/abs/0912.2075">Isotypic Decomposition of the Cohomology and Factorization of the Zeta Functions of Dwork Hypersurfaces</a>, arXiv:0912.2075 [math.NT], 2009.
%p A081216 a:= n-> (n^n-(-1)^n)/(n+1):
%p A081216 seq(a(n), n=0..20); # _Alois P. Heinz_, May 11 2023
%o A081216 (Sage) [((n - 1)**(n - 1) + (-1)**n) // n for n in range(1, 16)]
%o A081216 (PARI) a(n) = (n^n-(-1)^n)/(n+1); \\ _Michel Marcus_, Jul 29 2017
%Y A081216 Main diagonal of A062160.
%Y A081216 Cf. A056826, A124899, A014566 (Sierpinski numbers of the first kind: n^n + 1).
%K A081216 easy,nonn
%O A081216 0,4
%A A081216 _Vladeta Jovovic_, Apr 17 2003
%E A081216 Edited by _F. Chapoton_, Feb 03 2011