A242163 Number of ascent sequences of length n with exactly ten flat steps.

1, 11, 132, 1430, 16016, 183183, 2170168, 26682656, 341093610, 4535113154, 62703599816, 901046882736, 13446991930372, 208232533802370, 3342841274221680, 55579584231437200, 956172212838496225, 17004878491751993700, 312343867479847052850, 5920144379977393205640

Offset

11,2

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 11..140

Formula

a(n) ~ Pi^(35/2) / (10! * 6^8 * 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, 10]; Table[a[n], {n, 11, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Crossrefs

Column k=10 of A242153.

Sequence in context: A044041 A158536 A229252 * A105280 A196731 A289415

Adjacent sequences: A242160 A242161 A242162 * A242164 A242165 A242166

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Status

approved