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A261785 Sum over all Motzkin paths of length n of products over all peaks p of (n*x_p+y_p)/y_p, where x_p and y_p are the coordinates of peak p. 2
1, 1, 4, 13, 101, 571, 6735, 54713, 873019, 9274471, 187278048, 2460190261, 60205154959, 942541045811, 27121249048036, 492972449490417, 16312991079531595, 337650093459084079, 12633283010644517490, 293339323822142071021, 12245145846336974734339 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

Wikipedia, Motzkin number

FORMULA

a(n) = A258309(n,n).

MAPLE

b:= proc(x, y, t, k) option remember; `if`(y>x or y<0, 0,

      `if`(x=0, 1, b(x-1, y-1, false, k)*`if`(t, (k*x+y)/y, 1)

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

    end:

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

seq(a(n), n=0..25);

CROSSREFS

Main diagonal of A258309.

Sequence in context: A041433 A222764 A058014 * A276912 A045886 A015460

Adjacent sequences:  A261782 A261783 A261784 * A261786 A261787 A261788

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 31 2015

STATUS

approved

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Last modified May 23 18:42 EDT 2017. Contains 286926 sequences.