A242156 Number of ascent sequences of length n with exactly three flat steps.

1, 4, 20, 100, 560, 3416, 22764, 164640, 1286175, 10800460, 97064396, 929872944, 9461716810, 101926129200, 1159018540400, 13874662175520, 174430929675615, 2297878921894800, 31655403616078550, 455168137467988560, 6819445400385661890, 106288470495749772120

Offset: 4

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 = 4..140

Crossrefs

Column k=3 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, 3]; Table[a[n], {n, 4, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Formula

a(n) ~ Pi^(7/2)/(36*sqrt(3)*exp(Pi^2/12)) * (6/Pi^2)^n * n! * sqrt(n). - Vaclav Kotesovec, Aug 27 2014