A242156 Number of ascent sequences of length n with exactly three flat steps.

1, 4, 20, 100, 560, 3416, 22764, 164640, 1286175, 10800460, 97064396, 929872944, 9461716810, 101926129200, 1159018540400, 13874662175520, 174430929675615, 2297878921894800, 31655403616078550, 455168137467988560, 6819445400385661890, 106288470495749772120

Offset

4,2

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 4..140

Formula

a(n) ~ Pi^(7/2)/(36*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, 3]; Table[a[n], {n, 4, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Crossrefs

Column k=3 of A242153.

Sequence in context: A370536 A216099 A105480 * A186369 A093440 A168606

Adjacent sequences: A242153 A242154 A242155 * A242157 A242158 A242159

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Status

approved