A242160 Number of ascent sequences of length n with exactly seven flat steps.

1, 8, 72, 600, 5280, 48312, 465036, 4708704, 50160825, 561623920, 6600378928, 81297463104, 1047817553016, 14109488456400, 198192170408400, 2899804394683680, 44131025207930595, 697636040687261280, 11441167306954104500, 194421818718469399200

Offset

8,2

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 8..140

Formula

a(n) ~ Pi^(23/2) / (7! * 6^5 * 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, 7]; Table[a[n], {n, 8, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Crossrefs

Column k=7 of A242153.

Sequence in context: A246940 A158798 A229249 * A343365 A062541 A057091

Adjacent sequences: A242157 A242158 A242159 * A242161 A242162 A242163

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Status

approved