A178922 a(n) = (n+1)^n - n^(n-1) for n > 0, a(0) = 1.

1, 1, 7, 55, 561, 7151, 109873, 1979503, 40949569, 956953279, 24937424601, 717070946087, 22555076751793, 770416688131663, 28399211252136481, 1123728578581456351, 47508270371060021505, 2137250367863029663487, 101941438738172545000873, 5138752649702088758467159

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Dec 29 2010

Keywords

• nonn

Crossrefs

Cf. A000169, A007925, A084363, A152917.

Programs

Maple

a:= n-> (f-> f(n+1)-f(n))(n-> `if`(n=0, 0, n^(n-1))):
seq(a(n), n=0..20);  # Alois P. Heinz, Feb 26 2020

Mathematica

Table[(n+1)^n-n^(n-1),{n,25}]

Maxima

A178922[n]:=(n+1)^n-n^(n-1)$ makelist(A178922[n],n,1,30); /* Martin Ettl, Oct 29 2012 */

PARI

vector(100, n, (n+1)^n - n^(n-1)) \\ Altug Alkan, Oct 19 2015

Formula

a(n) = A152917(n+1) - A152917(n). - Alexei Kourbatov, Oct 19 2015

E.g.f.: W(-x) - W(-x)/(x*(1+W(-x))) where W is the Lambert W function. - Robert Israel, Oct 19 2015

Extensions

a(0)=1 prepended and definition adapted by Alois P. Heinz, Feb 26 2020