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%I #9 Feb 10 2015 06:55:20
%S 1,9,90,825,7920,78507,813813,8828820,100321650,1193450830,
%T 14850852588,193081474872,2619543882540,37037407198050,
%U 545028468623100,8336937634715580,132393075623791785,2180112627147691500,37183793747600839625,656173638174834222300
%N Number of ascent sequences of length n with exactly eight flat steps.
%H Joerg Arndt and Alois P. Heinz, <a href="/A242161/b242161.txt">Table of n, a(n) for n = 9..140</a>
%F a(n) ~ Pi^(27/2) / (8! * 6^6 * 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, 8]; Table[a[n], {n, 9, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A242153 *)
%Y Column k=8 of A242153.
%K nonn
%O 9,2
%A _Joerg Arndt_ and _Alois P. Heinz_, May 05 2014