A242164 - OEIS

%I #17 Feb 10 2015 08:44:45

%S 1,1,3,20,175,2016,28182,465036,8828820,189496450,4535113154,

%T 119706872376,3454013050488,108140144894600,3650830138093500,

%U 132194177662402800,5110163818369981650,210037720563156731850,9146299175093615073000,420627290039763259876500

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

%H Joerg Arndt and Alois P. Heinz, <a href="/A242164/b242164.txt">Table of n, a(n) for n = 0..70</a>

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

%F a(n) ~ 6*sqrt(3) / (Pi^3 * exp(Pi^2/12)) * (24/Pi^2)^n * n!. - _Vaclav Kotesovec_, Aug 28 2014

%e a(0) = 1: the empty sequence.

%e a(1) = 1: [0,0].

%e a(2) = 3: [0,0,0,1], [0,0,1,1], [0,1,1,1].

%e 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].

%t 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 *)

%Y Cf. A242153.

%K nonn

%O 0,3

%A _Joerg Arndt_ and _Alois P. Heinz_, May 05 2014