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 A258180 Sum over all Dyck paths of semilength n of products over all peaks p of C(x_p,y_p), where x_p and y_p are the coordinates of peak p. 10
 1, 1, 4, 33, 517, 15326, 852912, 91023697, 19716262702, 8794395041567, 8016790849841585, 15556074485786226848, 64891787190080888991273, 561815453349204340865790817, 10402242033224422585780623039909, 423787530114579490372987256671625678 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A Dyck path of semilength n is a (x,y)-lattice path from (0,0) to (2n,0) that does not go below the x-axis and consists of steps U=(1,1) and D=(1,-1). A peak of a Dyck path is any lattice point visited between two consecutive steps UD. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..75 Wikipedia, Lattice path MAPLE b:= proc(x, y, t) option remember; `if`(y>x or y<0, 0, `if`(x=0, 1, b(x-1, y-1, false)*`if`(t, binomial(x, y), 1) + b(x-1, y+1, true) )) end: a:= n-> b(2*n, 0, false): seq(a(n), n=0..20); MATHEMATICA b[x_, y_, t_] := b[x, y, t] = If[y > x || y < 0, 0, If[x == 0, 1, b[x - 1, y - 1, False]*If[t, Binomial[x, y], 1] + b[x - 1, y + 1, True]]]; a[n_] := b[2*n, 0, False]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Apr 23 2016, translated from Maple *) CROSSREFS Cf. A000108, A000698, A005411, A005412, A258172, A258173, A258174, A258175, A258176, A258177, A258178, A258179, A258181. Sequence in context: A002018 A368837 A219504 * A072754 A225609 A113086 Adjacent sequences: A258177 A258178 A258179 * A258181 A258182 A258183 KEYWORD nonn AUTHOR Alois P. Heinz, May 22 2015 STATUS approved

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Last modified September 16 02:52 EDT 2024. Contains 375959 sequences. (Running on oeis4.)