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 A288141 Number of Dyck paths of semilength n such that the number of peaks is strongly decreasing from lower to higher levels. 4
 1, 1, 1, 1, 4, 5, 10, 22, 46, 148, 324, 722, 1843, 4634, 12537, 34248, 95711, 266761, 724689, 1983267, 5553902, 15900083, 46201546, 135511171, 400668869, 1189723253, 3535186203, 10516298421, 31405658622, 94378367065, 285623516777, 870481565252, 2671088133010 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 Wikipedia, Counting lattice paths EXAMPLE a(5) = 5:                      /\        /\        /\        /\   /\/\/\/\/\  /\/\/\/  \  /\/\/  \/\  /\/  \/\/\  /  \/\/\/\ MAPLE b:= proc(n, k, j) option remember; `if`(n=j, 1, add(add(        b(n-j, t, i)*binomial(i, t)*binomial(j-1, i-1-t),        t=max(k+1, i-j)..min(n-j, i-1)), i=1..n-j))     end: a:= n-> `if`(n=0, 1, add(b(n, k\$2), k=1..n)): seq(a(n), n=0..34); MATHEMATICA b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[Sum[b[n - j, t, i]* Binomial[i, t]*Binomial[j - 1, i - 1 - t], {t, Max[k + 1, i - j], Min[n - j, i - 1]}], {i, 1, n - j}]]; a[n_] := If[n == 0, 1, Sum[b[n, k, k], {k, 1, n}]]; Table[a[n], {n, 0, 34}] (* Jean-François Alcover, May 29 2018, from Maple *) CROSSREFS Cf. A000108, A008930, A048285, A288140, A288146, A288147. Sequence in context: A049898 A166577 A242960 * A203853 A109675 A052508 Adjacent sequences:  A288138 A288139 A288140 * A288142 A288143 A288144 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 05 2017 STATUS approved

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Last modified May 25 11:07 EDT 2020. Contains 334592 sequences. (Running on oeis4.)