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A258312 Sum over all Motzkin paths of length n of products over all peaks p of x_p/y_p, where x_p and y_p are the coordinates of peak p. 3
1, 1, 2, 5, 14, 43, 141, 490, 1785, 6789, 26809, 109632, 462755, 2012441, 8997402, 41297927, 194306557, 936082502, 4612095475, 23219012907, 119328025012, 625545408219, 3342370197206, 18190297736313, 100768960522871, 567886743369378, 3253833477309093 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..800

Wikipedia, Motzkin number

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, x/y, 1)

                  +b(x-1, y, false)+b(x-1, y+1, true)))

    end:

a:= n-> b(n, 0, false):

seq(a(n), n=0..30);

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, x/y, 1] + b[x-1, y, False] + b[x-1, y+1, True]]];

a[n_] := b[n, 0, False];

Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Jun 10 2017, translated from Maple *)

CROSSREFS

Column k=0 of A258306 and A258307.

Sequence in context: A029889 A307787 A221586 * A123020 A005317 A126566

Adjacent sequences:  A258309 A258310 A258311 * A258313 A258314 A258315

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 25 2015

STATUS

approved

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Last modified October 17 02:04 EDT 2019. Contains 328106 sequences. (Running on oeis4.)