A242161 Number of ascent sequences of length n with exactly eight flat steps.

1, 9, 90, 825, 7920, 78507, 813813, 8828820, 100321650, 1193450830, 14850852588, 193081474872, 2619543882540, 37037407198050, 545028468623100, 8336937634715580, 132393075623791785, 2180112627147691500, 37183793747600839625, 656173638174834222300

Offset: 9

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 = 9..140

Crossrefs

Column k=8 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, 8]; Table[a[n], {n, 9, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Formula

a(n) ~ Pi^(27/2) / (8! * 6^6 * sqrt(3)*exp(Pi^2/12)) * (6/Pi^2)^n * n! * sqrt(n). - Vaclav Kotesovec, Aug 27 2014