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

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 = 2..140

Crossrefs

Column k=1 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, 1]; Table[ a[n], {n, 2, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Formula

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