A081216 a(n) = (n^n-(-1)^n)/(n+1).

0, 1, 1, 7, 51, 521, 6665, 102943, 1864135, 38742049, 909090909, 23775972551, 685853880635, 21633936185161, 740800455037201, 27368368148803711, 1085102592571150095, 45957792327018709121, 2070863582910344082917, 98920982783015679456199

Offset: 0

Author

Vladeta Jovovic, Apr 17 2003

Keywords

• easy
• nonn

Comments

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

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]

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..387
• Philippe Goutet, Isotypic Decomposition of the Cohomology and Factorization of the Zeta Functions of Dwork Hypersurfaces, arXiv:0912.2075 [math.NT], 2009.

Crossrefs

Main diagonal of A062160.

Cf. A056826, A124899, A014566 (Sierpinski numbers of the first kind: n^n + 1).

Programs

Maple

a:= n-> (n^n-(-1)^n)/(n+1):
seq(a(n), n=0..20);  # Alois P. Heinz, May 11 2023

PARI

a(n) = (n^n-(-1)^n)/(n+1); \\ Michel Marcus, Jul 29 2017

Sage

[((n - 1)**(n - 1) + (-1)**n) // n for n in range(1, 16)]

Extensions

Edited by F. Chapoton, Feb 03 2011