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%I #9 Feb 10 2015 06:55:08
%S 1,7,56,420,3360,28182,250404,2354352,23408385,245710465,2717803088,
%T 31615680096,386038045848,4938320959740,66064056802800,
%U 922665034672080,13431181585022355,203477178533784540,3203526845947149260,52344335808818684400,886527902050136045700
%N Number of ascent sequences of length n with exactly six flat steps.
%H Joerg Arndt and Alois P. Heinz, <a href="/A242159/b242159.txt">Table of n, a(n) for n = 7..140</a>
%F a(n) ~ Pi^(19/2) / (6! * 6^4 * 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, 6]; Table[a[n], {n, 7, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A242153 *)
%Y Column k=6 of A242153.
%K nonn
%O 7,2
%A _Joerg Arndt_ and _Alois P. Heinz_, May 05 2014