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%I #9 Feb 10 2015 06:54:50
%S 1,4,20,100,560,3416,22764,164640,1286175,10800460,97064396,929872944,
%T 9461716810,101926129200,1159018540400,13874662175520,174430929675615,
%U 2297878921894800,31655403616078550,455168137467988560,6819445400385661890,106288470495749772120
%N Number of ascent sequences of length n with exactly three flat steps.
%H Joerg Arndt and Alois P. Heinz, <a href="/A242156/b242156.txt">Table of n, a(n) for n = 4..140</a>
%F a(n) ~ Pi^(7/2)/(36*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, 3]; Table[a[n], {n, 4, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A242153 *)
%Y Column k=3 of A242153.
%K nonn
%O 4,2
%A _Joerg Arndt_ and _Alois P. Heinz_, May 05 2014
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