A246249 Number of permutations of [n] with exactly four occurrences of the consecutive step pattern up, down, down.

3052323, 186723630, 7683652710, 260901740745, 8002149813810, 231524173618290, 6486876741415365, 178899784802719290, 4910005699045578270, 135118835430805648215, 3748167756629344500390, 105205858082972481706290, 2996195115836815163207370

Offset: 13

Author

Alois P. Heinz, Aug 20 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 13..160

Crossrefs

Column k=4 of A242819.

Formula

a(n) ~ c * (3*sqrt(3)/(2*Pi))^n * n! * n^4, where c = 0.000882722753946826148... = c0 * (c0-1)^4 / (3^4 * 4!), and c0 = (1 + exp(Pi/sqrt(3))) * sqrt(3) / (2*Pi). - Vaclav Kotesovec, Aug 26 2014