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

2,1

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]

Links

Table of n, a(n) for n=2..21.

Mikhail Gaichenkov, The property of Kendall-Mann numbers, answered by Richard Stanley, 2010

Mikhail Gaichenkov, A combinatorial proof for the property of KM numbers?

Formula

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

Example

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

Crossrefs

Cf. A000140.

Sequence in context: A087164 A077213 A112601 * A205827 A098544 A176706

Adjacent sequences: A181606 A181607 A181608 * A181610 A181611 A181612

Keyword

nonn

Author

Mikhail Gaichenkov, Jan 30 2011

Status

approved