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Number of ascent sequences of length n with exactly seven flat steps.
3

%I #9 Feb 10 2015 06:55:14

%S 1,8,72,600,5280,48312,465036,4708704,50160825,561623920,6600378928,

%T 81297463104,1047817553016,14109488456400,198192170408400,

%U 2899804394683680,44131025207930595,697636040687261280,11441167306954104500,194421818718469399200

%N Number of ascent sequences of length n with exactly seven flat steps.

%H Joerg Arndt and Alois P. Heinz, <a href="/A242160/b242160.txt">Table of n, a(n) for n = 8..140</a>

%F a(n) ~ Pi^(23/2) / (7! * 6^5 * 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, 7]; Table[a[n], {n, 8, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A242153 *)

%Y Column k=7 of A242153.

%K nonn

%O 8,2

%A _Joerg Arndt_ and _Alois P. Heinz_, May 05 2014