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A242156 Number of ascent sequences of length n with exactly three flat steps. 3
1, 4, 20, 100, 560, 3416, 22764, 164640, 1286175, 10800460, 97064396, 929872944, 9461716810, 101926129200, 1159018540400, 13874662175520, 174430929675615, 2297878921894800, 31655403616078550, 455168137467988560, 6819445400385661890, 106288470495749772120 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 4..140

FORMULA

a(n) ~ Pi^(7/2)/(36*sqrt(3)*exp(Pi^2/12)) * (6/Pi^2)^n * n! * sqrt(n). - Vaclav Kotesovec, Aug 27 2014

MATHEMATICA

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-Fran├žois Alcover, Feb 10 2015, after A242153 *)

CROSSREFS

Column k=3 of A242153.

Sequence in context: A005054 A216099 A105480 * A186369 A093440 A168606

Adjacent sequences:  A242153 A242154 A242155 * A242157 A242158 A242159

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, May 05 2014

STATUS

approved

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Last modified March 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)