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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); MATHEMATICA b[x_, y_, t_, k_] := b[x, y, t, k] = If[y > x || 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]]]; a[n_] := b[n, 0, False, n]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jun 10 2017, translated from Maple *) CROSSREFS Main diagonal of A258309. Sequence in context: A222764 A058014 A290392 * 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 August 20 17:05 EDT 2017. Contains 290836 sequences.