A242159 Number of ascent sequences of length n with exactly six flat steps.

1, 7, 56, 420, 3360, 28182, 250404, 2354352, 23408385, 245710465, 2717803088, 31615680096, 386038045848, 4938320959740, 66064056802800, 922665034672080, 13431181585022355, 203477178533784540, 3203526845947149260, 52344335808818684400, 886527902050136045700

Offset: 7

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 = 7..140

Crossrefs

Column k=6 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, 6]; Table[a[n], {n, 7, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Formula

a(n) ~ Pi^(19/2) / (6! * 6^4 * sqrt(3)*exp(Pi^2/12)) * (6/Pi^2)^n * n! * sqrt(n). - Vaclav Kotesovec, Aug 27 2014