A242162 Number of ascent sequences of length n with exactly nine flat steps.

1, 10, 110, 1100, 11440, 122122, 1356355, 15695680, 189496450, 2386901660, 31351799908, 429069944160, 6112269059260, 90535884261900, 1392850530925700, 22231833692574880, 367758543399421625, 6298103145093331000, 111551381242802518875, 2041429096543928691600

Offset

10,2

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 10..140

Formula

a(n) ~ Pi^(31/2) / (9! * 6^7 * 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, 9]; Table[a[n], {n, 10, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Crossrefs

Column k=9 of A242153.

Sequence in context: A290417 A289405 A285768 * A144099 A102092 A288899

Adjacent sequences: A242159 A242160 A242161 * A242163 A242164 A242165

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Status

approved