A292694 Sum over all Dyck paths of semilength 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.

1, 2, 24, 764, 47650, 4953222, 776036520, 171140340632, 50569280587134, 19291547098210250, 9231053150452094896, 5414004448824367167444, 3819333773584571070766756, 3190486349393577447421521614, 3114480787139044226695876470000, 3512892958123523912923517986350000

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Wikipedia, Lattice path

Formula

a(n) = A258222(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+1, true, k)  ))
    end:
a:= n-> b(2*n, 0, false, n):
seq(a(n), n=0..18);

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 + 1, True, k]]];
a[n_] := b[2n, 0, False, n];
Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Jun 02 2018, from Maple *)

Crossrefs

Main diagonal of A258222.

Sequence in context: A009396 A338188 A274634 * A012128 A099704 A265879

Adjacent sequences: A292691 A292692 A292693 * A292695 A292696 A292697

Keyword

nonn

Author

Alois P. Heinz, Sep 20 2017

Status

approved