A242157 Number of ascent sequences of length n with exactly four flat steps.

1, 5, 30, 175, 1120, 7686, 56910, 452760, 3858525, 35101495, 339725386, 3487023540, 37846867240, 433186049100, 5215583431800, 65904645333720, 872154648378075, 12063864339947700, 174104719888432025, 2617216790440934220, 40916672402313971340

Offset: 5

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 = 5..140

Crossrefs

Column k=4 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, 4]; Table[a[n], {n, 5, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Formula

a(n) ~ Pi^(11/2)/(864*sqrt(3)*exp(Pi^2/12)) * (6/Pi^2)^n * n! * sqrt(n). - Vaclav Kotesovec, Aug 27 2014