A232545 Number of Euler tours of the complete digraph on n vertices.

1, 3, 256, 972000, 247669456896, 6022251970560000000, 18932148110851728998400000000, 10036271333655026636037644353536000000000, 1135547314049215265041779022180122624000000000000000000, 33878761698754076709292639330840075944838638855101181276979200000000000

Offset: 2

Author

Tomas Boothby, Nov 25 2013

Keywords

• nonn
• walk

Examples

			For n = 2, there is one Euler tour, (1,2,1), since (1,2,1) is cyclically equivalent to (2,1,2).
For n = 3, there are three Euler tours: (1,2,1,3,2,3,1), (1,2,3,1,3,2,1), (1,2,3,2,1,3,1).
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..30
• Wikipedia, BEST Theorem, a formula for counting Euler tours in digraphs.

Programs

PARI

a(n) = n^(n-2)*(n-2)!^n \\ Andrew Howroyd, Dec 28 2021

Formula

a(n) = n^(n-2)*(n-2)!^n, by the "BEST Theorem". - James Thompson, Jul 18 2017, Günter Rote, Dec 09 2021

The above formula can be written as a(n) = A000272(n)*A000142(n-2)^n. - Omar E. Pol, Jul 18 2017

Extensions

a(5) corrected by Tomas Boothby, Dec 03 2013

Terms a(8) and beyond from Andrew Howroyd, Dec 28 2021