A242158 Number of ascent sequences of length n with exactly five flat steps.

1, 6, 42, 280, 2016, 15372, 125202, 1086624, 10032165, 98284186, 1019176158, 11158475328, 128679348616, 1559469776760, 19819217040840, 263618581334880, 3663049523187915, 53081003095769880, 800881711486787315, 12562640594116484256, 204583362011569856700

Offset

6,2

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 6..140

Formula

a(n) ~ Pi^(15/2)/(25920*sqrt(3)*exp(Pi^2/12)) * (6/Pi^2)^n * n! * sqrt(n). - Vaclav Kotesovec, Aug 27 2014

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, Expand[Sum[ If[j == i, x, 1]*b[n - 1, j, t + If[j > i, 1, 0]], {j, 0, t + 1}]]]; a[n_] := Coefficient[b[n, -1, -1], x, 5]; Table[a[n], {n, 6, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Crossrefs

Column k=5 of A242153.

Sequence in context: A062310 A229247 A105482 * A157335 A057089 A110711

Adjacent sequences: A242155 A242156 A242157 * A242159 A242160 A242161

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Status

approved