A246253 Number of permutations of [n] with exactly eight occurrences of the consecutive step pattern up, down, down.

4736552519729393091, 925712659777722254622, 108450427756505074280046, 9790367872313042801164557, 752566904329661335915465770, 51895294413875186427307822050, 3313685917841456847408819072255, 200074814234955942882986408262750, 11591748407639299505418556743604770

Offset: 25

Author

Alois P. Heinz, Aug 20 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 25..160

Crossrefs

Column k=8 of A242819.

Formula

a(n) ~ c * (3*sqrt(3)/(2*Pi))^n * n! * n^8, where c = 0.00000000566049683079281633... = c0 * (c0-1)^8 / (3^8 * 8!), and c0 = (1 + exp(Pi/sqrt(3))) * sqrt(3) / (2*Pi). - Vaclav Kotesovec, Aug 26 2014