A242159 Number of ascent sequences of length n with exactly six flat steps.

1, 7, 56, 420, 3360, 28182, 250404, 2354352, 23408385, 245710465, 2717803088, 31615680096, 386038045848, 4938320959740, 66064056802800, 922665034672080, 13431181585022355, 203477178533784540, 3203526845947149260, 52344335808818684400, 886527902050136045700

Offset

7,2

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 7..140

Formula

a(n) ~ Pi^(19/2) / (6! * 6^4 * 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, 6]; Table[a[n], {n, 7, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Crossrefs

Column k=6 of A242153.

Sequence in context: A092318 A092315 A229248 * A057090 A156362 A055274

Adjacent sequences: A242156 A242157 A242158 * A242160 A242161 A242162

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Status

approved