This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A242164 #17 Feb 10 2015 08:44:45
%S A242164 1,1,3,20,175,2016,28182,465036,8828820,189496450,4535113154,
%T A242164 119706872376,3454013050488,108140144894600,3650830138093500,
%U A242164 132194177662402800,5110163818369981650,210037720563156731850,9146299175093615073000,420627290039763259876500
%N A242164 Number of ascent sequences of length 2n with exactly n flat steps.
%H A242164 Joerg Arndt and Alois P. Heinz, <a href="/A242164/b242164.txt">Table of n, a(n) for n = 0..70</a>
%F A242164 a(n) = A242153(2n,n).
%F A242164 a(n) ~ 6*sqrt(3) / (Pi^3 * exp(Pi^2/12)) * (24/Pi^2)^n * n!. - _Vaclav Kotesovec_, Aug 28 2014
%e A242164 a(0) = 1: the empty sequence.
%e A242164 a(1) = 1: [0,0].
%e A242164 a(2) = 3: [0,0,0,1], [0,0,1,1], [0,1,1,1].
%e A242164 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 A242164 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 A242164 Cf. A242153.
%K A242164 nonn
%O A242164 0,3
%A A242164 _Joerg Arndt_ and _Alois P. Heinz_, May 05 2014