A246250 Number of permutations of [n] with exactly five occurrences of the consecutive step pattern up, down, down.

1620265923, 142031290158, 8039798211078, 366995453376294, 14827018289073804, 555488440936519572, 19848769453749875607, 688735406876831016606, 23495176763112174568146, 794853120296757717355104, 26836227616917587293450368, 908479209956520414451380624

Offset: 16

Author

Alois P. Heinz, Aug 20 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 16..160

Crossrefs

Column k=5 of A242819.

Formula

a(n) ~ c * (3*sqrt(3)/(2*Pi))^n * n! * n^5, where c = 0.00005687732922585807984... = c0 * (c0-1)^5 / (3^5 * 5!), and c0 = (1 + exp(Pi/sqrt(3))) * sqrt(3) / (2*Pi). - Vaclav Kotesovec, Aug 26 2014