A061190 a(n) = n^n - n.

1, 0, 2, 24, 252, 3120, 46650, 823536, 16777208, 387420480, 9999999990, 285311670600, 8916100448244, 302875106592240, 11112006825558002, 437893890380859360, 18446744073709551600, 827240261886336764160, 39346408075296537575406, 1978419655660313589123960

Offset: 0

Author

Lawrence H. Shirley (LShirley(AT)towson.edu), May 30 2001

Keywords

• nonn
• easy

Comments

Number of endofunctions on [n] such that no element has a preimage of cardinality n. - Alois P. Heinz, Jul 21 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Main diagonal of A245405.

Programs

Magma

[n^n - n : n in [0..20]]; // Vincenzo Librandi, Sep 01 2011

Mathematica

Table[n^n-n, {n,25}] (* Vladimir Joseph Stephan Orlovsky, Dec 28 2010 *)

Formula

E.g.f.: 1/(1 + LambertW(-x)) - x*exp(x), where LambertW() is the Lambert W-function. - Ilya Gutkovskiy, Feb 08 2017

a(n) = n*A037205(n-1). - R. J. Mathar, Jul 02 2017

Extensions

a(0)=1 inserted by Alois P. Heinz, Jul 21 2014