A242155 Number of ascent sequences of length n with exactly two flat steps.

1, 3, 12, 50, 240, 1281, 7588, 49392, 350775, 2700115, 22399476, 199258488, 1892343362, 19111149225, 204532683600, 2312443695920, 27541725738255, 344681838284220, 4522200516582650, 62068382381998440, 889492878311173290, 13286058811968721515

Offset: 3

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 = 3..140

Crossrefs

Column k=2 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, 2]; Table[a[n], {n, 3, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Formula

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