OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
Wikipedia, Counting lattice paths
EXAMPLE
a(5) = 5:
/\ /\ /\ /\
/\/\/\/\/\ /\/\/\/ \ /\/\/ \/\ /\/ \/\/\ / \/\/\/\
MAPLE
b:= proc(n, k, j) option remember; `if`(n=j, 1, add(add(
b(n-j, t, i)*binomial(i, t)*binomial(j-1, i-1-t),
t=max(k+1, i-j)..min(n-j, i-1)), i=1..n-j))
end:
a:= n-> `if`(n=0, 1, add(b(n, k$2), k=1..n)):
seq(a(n), n=0..34);
MATHEMATICA
b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[Sum[b[n - j, t, i]* Binomial[i, t]*Binomial[j - 1, i - 1 - t], {t, Max[k + 1, i - j], Min[n - j, i - 1]}], {i, 1, n - j}]];
a[n_] := If[n == 0, 1, Sum[b[n, k, k], {k, 1, n}]];
Table[a[n], {n, 0, 34}] (* Jean-François Alcover, May 29 2018, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 05 2017
STATUS
approved