A242154 Number of ascent sequences of length n with exactly one flat step.

1, 2, 6, 20, 80, 366, 1897, 10976, 70155, 490930, 3733246, 30655152, 270334766, 2548153230, 25566585450, 272052199520, 3060191748695, 36282298766760, 452220051658265, 5911274512571280, 80862988937379390, 1155309461910323610, 17208404375488550100

Offset

2,2

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 2..140

Formula

a(n) ~ 2*sqrt(3)/(exp(Pi^2/12)*sqrt(Pi)) * (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, 1]; Table[ a[n], {n, 2, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Crossrefs

Column k=1 of A242153.

Sequence in context: A144168 A177482 A300011 * A108124 A186365 A245373

Adjacent sequences: A242151 A242152 A242153 * A242155 A242156 A242157

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Status

approved