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

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Keywords

• nonn

Links

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

Crossrefs

Column k=9 of A242153.

Programs

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 *)

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