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 A287846 Number of Dyck paths of semilength n such that each positive level up to the highest nonempty level has exactly one peak. 9
 1, 1, 0, 2, 0, 4, 6, 8, 24, 52, 96, 212, 504, 1072, 2352, 5288, 11928, 26800, 60336, 136304, 308928, 701248, 1593120, 3622016, 8245008, 18787360, 42836928, 97724384, 223052784, 509338816, 1163512032, 2658731648, 6077117376, 13893874624, 31771515648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS All terms with n > 1 are even. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Wikipedia, Counting lattice paths EXAMPLE . a(1) = 1:    /\  . . . a(3) = 2:     /\       /\ .            /\/  \     /  \/\  . . . a(5) = 4: .                /\       /\         /\       /\ .             /\/  \     /  \/\   /\/  \     /  \/\ .          /\/      \ /\/      \ /      \/\ /      \/\ . MAPLE b:= proc(n, j) option remember; `if`(n=j or n=0, 1, add(        b(n-j, i)*binomial(j-1, i-2)*i, i=1..min(j+2, n-j)))     end: a:= n-> b(n, 1): seq(a(n), n=0..35); MATHEMATICA b[n_, j_] := b[n, j] = If[n == j || n == 0, 1, Sum[b[n - j, i]*Binomial[j - 1, i - 2]*i, {i, 1, Min[j + 2, n - j]}]]; a[n_] := b[n, 1]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, May 23 2018, translated from Maple *) CROSSREFS Column k=1 of A288318. Cf. A000108, A281874, A287843, A287845, A287901, A287963, A287987, A289020. Sequence in context: A196877 A098123 A066659 * A085623 A317965 A190791 Adjacent sequences:  A287843 A287844 A287845 * A287847 A287848 A287849 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 01 2017 STATUS approved

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Last modified September 18 17:02 EDT 2020. Contains 337170 sequences. (Running on oeis4.)