A246248 Number of permutations of [n] with exactly three occurrences of the consecutive step pattern up, down, down.

11259, 443718, 12450834, 297195804, 6589314360, 141014406600, 2982538767870, 63210091744620, 1354523537530620, 29518995185712180, 656767731733672680, 14956075051814966040, 349170616179434073825, 8366057002343951876610, 205839505389444095064510

Offset: 10

Author

Alois P. Heinz, Aug 20 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..160

Crossrefs

Column k=3 of A242819.

Formula

a(n) ~ c * (3*sqrt(3)/(2*Pi))^n * n! * n^3, where c = 0.01095971939528021798... = c0 * (c0-1)^3 / (3^3 * 3!), and c0 = (1 + exp(Pi/sqrt(3))) * sqrt(3) / (2*Pi). - Vaclav Kotesovec, Aug 26 2014