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

5,2

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 5..140

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

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 *)

Crossrefs

Column k=4 of A242153.

Sequence in context: A057088 A156195 A105481 * A094167 A051738 A052934

Adjacent sequences: A242154 A242155 A242156 * A242158 A242159 A242160

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Status

approved