A246252 Number of permutations of [n] with exactly seven occurrences of the consecutive step pattern up, down, down.

2172534146099019, 336291324862551606, 31816048233798681066, 2348418329934108057072, 149140942861163014893024, 8573289075750149662810032, 460018114299281721089786796, 23509721961960146267578379640, 1160583084129910496820714859320

Offset: 22

Author

Alois P. Heinz, Aug 20 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 22..160

Crossrefs

Column k=7 of A242819.

Formula

a(n) ~ c * (3*sqrt(3)/(2*Pi))^n * n! * n^7, where c = 0.0000001405593242634352116... = c0 * (c0-1)^7 / (3^7 * 7!), and c0 = (1 + exp(Pi/sqrt(3))) * sqrt(3) / (2*Pi). - Vaclav Kotesovec, Aug 26 2014