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 A287987 Number of Dyck paths of semilength n such that all positive levels have the same number of peaks. 6
 1, 1, 1, 3, 1, 8, 13, 13, 54, 132, 280, 547, 1219, 3904, 11107, 25082, 53777, 137751, 419831, 1257599, 3453557, 8911341, 22636845, 59890162, 172264224, 529706648, 1630328686, 4765347773, 13125989799, 35253234315, 97531470556, 287880507391, 894915519516 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 Wikipedia, Counting lattice paths EXAMPLE . a(3) = 3:                         /\        /\ .                    /\/\/\      /\/  \      /  \/\  . . . a(5) = 8: .                       /\/\      /\/\      /\/\ .      /\/\/\/\/\  /\/\/    \  /\/    \/\  /    \/\/\ . .            /\        /\          /\        /\ .         /\/  \      /  \/\    /\/  \      /  \/\ .      /\/      \  /\/      \  /      \/\  /      \/\  . MAPLE b:= proc(n, k, j) option remember; `if`(n=j, 1,        add(binomial(i, k)*binomial(j-1, i-1-k)          *b(n-j, k, i), i=1+k..min(j+k, n-j)))     end: a:= n-> 1+add(b(n, j\$2), j=1..n/2): seq(a(n), n=0..33); MATHEMATICA b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[Binomial[i, k]*Binomial[j - 1, i - 1 - k]*b[n - j, k, i], {i, 1 + k, Min[j + k, n - j]}]]; a[n_] := 1 + Sum[b[n, j, j], {j, 1, n/2}]; Table[a[n], {n, 0, 33}] (* Jean-François Alcover, May 24 2018, translated from Maple *) CROSSREFS Row sums of A288318. Cf. A000108, A287845, A287846, A287993, A288109. Sequence in context: A019146 A102537 A131202 * A067955 A182509 A049965 Adjacent sequences:  A287984 A287985 A287986 * A287988 A287989 A287990 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 03 2017 STATUS approved

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Last modified January 19 15:37 EST 2020. Contains 331049 sequences. (Running on oeis4.)