A181609 Kendell-Mann numbers in terms of Mahonian distribution.

2, 3, 7, 23, 108, 604, 3980, 30186, 258969, 2479441, 26207604, 303119227, 3807956707, 51633582121, 751604592219, 11690365070546, 193492748067369, 3395655743755865, 62980031819261211, 1230967683216803500

Offset: 2

Author

Mikhail Gaichenkov, Jan 30 2011

Keywords

• nonn

Comments

It is well known that the variance of the Mahonian distribution is equal to sigma^2=n(n-1)(2n+5)/72. It is possible to have the asymptotic expansion for Kendell-Mann numbers M(n)=n!/sigma * 1/sqrt(2*Pi) * (1 - 2/(3*n) + O(1/n^2)). This results in M(n+1)/M(n)=n-1/2+O(1/n) as n--> infinity. [corrected by Vaclav Kotesovec, May 17 2015]

Examples

			M(2)=2, M(3)=3, M(4)=7,...
		

Links

• Mikhail Gaichenkov, The property of Kendall-Mann numbers, answered by Richard Stanley, 2010
• Mikhail Gaichenkov, A combinatorial proof for the property of KM numbers?

Crossrefs

Cf. A000140.

Formula

M(n) = Round(n!/sqrt(Pi*n(n-1)(2n+5)/36)).