

A181609


KendellMann numbers in terms of Mahonian distribution.


2



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

2,1


COMMENTS

It is well known that the variance of the Mahonian distribution is equal to sigma^2=n(n1)(2n+5)/72. It is possible to have the asymptotic expansion for KendellMann 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)=n1/2+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 KendallMann 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(n1)(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



