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 A288324 Number of Dyck paths of semilength n such that each positive level has exactly eight peaks. 2
 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 9, 315, 3465, 17325, 45045, 63063, 45045, 12870, 0, 81, 6075, 200340, 3835755, 48617415, 440531784, 3000152925, 15896972520, 67174514550, 230430986514, 649879542063, 1519950287430, 2963421671535, 4828750295985 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,18 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Wikipedia, Counting lattice paths MAPLE b:= proc(n, k, j) option remember;      `if`(n=j, 1, add(b(n-j, k, i)*(binomial(i, k)       *binomial(j-1, i-1-k)), i=1..min(j+k, n-j)))     end: a:= n-> `if`(n=0, 1, b(n, 8\$2)): seq(a(n), n=0..40); MATHEMATICA b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[b[n - j, k, i]*(Binomial[i, k]*Binomial[j - 1, i - 1 - k]), {i, 1, Min[j + k, n - j]}]]; a[n_] := If[n == 0, 1, b[n, 8, 8]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 02 2018, from Maple *) CROSSREFS Column k=8 of A288318. Cf. A000108. Sequence in context: A160194 A217145 A266835 * A317634 A198401 A135609 Adjacent sequences:  A288321 A288322 A288323 * A288325 A288326 A288327 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 07 2017 STATUS approved

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Last modified December 13 17:17 EST 2019. Contains 329970 sequences. (Running on oeis4.)