A242160 Number of ascent sequences of length n with exactly seven flat steps.

1, 8, 72, 600, 5280, 48312, 465036, 4708704, 50160825, 561623920, 6600378928, 81297463104, 1047817553016, 14109488456400, 198192170408400, 2899804394683680, 44131025207930595, 697636040687261280, 11441167306954104500, 194421818718469399200

Offset: 8

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 = 8..140

Crossrefs

Column k=7 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, 7]; Table[a[n], {n, 8, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Formula

a(n) ~ Pi^(23/2) / (7! * 6^5 * sqrt(3)*exp(Pi^2/12)) * (6/Pi^2)^n * n! * sqrt(n). - Vaclav Kotesovec, Aug 27 2014