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

3,2

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 3..140

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

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 *)

Crossrefs

Column k=2 of A242153.

Sequence in context: A268650 A151181 A094601 * A009024 A265083 A043291

Adjacent sequences: A242152 A242153 A242154 * A242156 A242157 A242158

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Status

approved