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

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Keywords

• nonn

Links

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

Crossrefs

Column k=5 of A242153.

Programs

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 *)

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