OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Wikipedia, Motzkin number
FORMULA
a(n) = Sum_{k=1..floor(n/2)} k * A097862(n,k).
MAPLE
b:= proc(x, y, h) option remember; `if`(x=0, h, add(
b(x-1, y+j, max(h, y)), j=-min(1, y)..min(1, x-y-1)))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..35);
MATHEMATICA
b[x_, y_, h_] := b[x, y, h] = If[x == 0, h, Sum[b[x - 1, y + j, Max[h, y]], {j, -Min[1, y], Min[1, x - y - 1]}]];
a[n_] := b[n, 0, 0];
a /@ Range[0, 35] (* Jean-François Alcover, May 10 2020, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 24 2020
STATUS
approved