A242164 Number of ascent sequences of length 2n with exactly n flat steps.

1, 1, 3, 20, 175, 2016, 28182, 465036, 8828820, 189496450, 4535113154, 119706872376, 3454013050488, 108140144894600, 3650830138093500, 132194177662402800, 5110163818369981650, 210037720563156731850, 9146299175093615073000, 420627290039763259876500

Offset

0,3

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..70

Formula

a(n) = A242153(2n,n).

a(n) ~ 6*sqrt(3) / (Pi^3 * exp(Pi^2/12)) * (24/Pi^2)^n * n!. - Vaclav Kotesovec, Aug 28 2014

Example

a(0) = 1: the empty sequence.
a(1) = 1: [0,0].
a(2) = 3: [0,0,0,1], [0,0,1,1], [0,1,1,1].
a(3) = 20: [0,0,0,0,1,0], [0,0,0,0,1,2], [0,0,0,1,0,0], [0,0,0,1,1,0], [0,0,0,1,1,2], [0,0,0,1,2,2], [0,0,1,0,0,0], [0,0,1,1,0,0], [0,0,1,1,1,0], [0,0,1,1,1,2], [0,0,1,1,2,2], [0,0,1,2,2,2], [0,1,0,0,0,0], [0,1,1,0,0,0], [0,1,1,1,0,0], [0,1,1,1,1,0], [0,1,1,1,1,2], [0,1,1,1,2,2], [0,1,1,2,2,2], [0,1,2,2,2,2].

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[2n, -1, -1], x, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Crossrefs

Cf. A242153.

Sequence in context: A154644 A321276 A000891 * A129840 A358214 A085390

Adjacent sequences: A242161 A242162 A242163 * A242165 A242166 A242167

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Status

approved