A086914 a(n) = ((n-1)^n/n)*Sum_{k>=1} (k^n/n^k).

0, 3, 11, 95, 1414, 31619, 980328, 39966975, 2063473712, 131165658459, 10041515879680, 909567637557215, 96070344004816128, 11688399779985830355, 1621144844290431509504, 254042974238965752088575

Offset

1,2

Comments

Appears to always be an integer.

Links

Table of n, a(n) for n=1..16.

Formula

a(n) = Euler(n, n)/(n-1) where Euler(n, x) is Eulerian polynomial of degree n (cf. A008292). - Vladeta Jovovic, Sep 26 2003

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

Prime p divides a(p-1) for p>2. - Alexander Adamchuk, Sep 19 2006

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

a(n) ~ exp(-1) * n! * n^(n-1) / log(n)^(n+1). - Vaclav Kotesovec, Jun 06 2022

Mathematica

Table[Sum[(n-1)^n*k^n/n^(k+1), {k, 1, Infinity}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 16 2016 *)

Crossrefs

Cf. A122020, A122778, A121376, A121985.

Sequence in context: A066384 A328810 A120587 * A123996 A201425 A008561

Adjacent sequences: A086911 A086912 A086913 * A086915 A086916 A086917

Keyword

nonn

Author

Benoit Cloitre, Sep 24 2003

Status

approved