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%I #9 Feb 10 2015 06:55:03
%S 1,6,42,280,2016,15372,125202,1086624,10032165,98284186,1019176158,
%T 11158475328,128679348616,1559469776760,19819217040840,
%U 263618581334880,3663049523187915,53081003095769880,800881711486787315,12562640594116484256,204583362011569856700
%N Number of ascent sequences of length n with exactly five flat steps.
%H Joerg Arndt and Alois P. Heinz, <a href="/A242158/b242158.txt">Table of n, a(n) for n = 6..140</a>
%F a(n) ~ Pi^(15/2)/(25920*sqrt(3)*exp(Pi^2/12)) * (6/Pi^2)^n * n! * sqrt(n). - _Vaclav Kotesovec_, Aug 27 2014
%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[n, -1, -1], x, 5]; Table[a[n], {n, 6, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A242153 *)
%Y Column k=5 of A242153.
%K nonn
%O 6,2
%A _Joerg Arndt_ and _Alois P. Heinz_, May 05 2014
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