OFFSET
0,7
COMMENTS
Also number of permutations of [n] with n nestings; also number of permutations of [n] with n crossings.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..300
FORMULA
a(n) = A263776(n,n).
MAPLE
b:= proc(u, o) option remember;
`if`(u+o=0, 1, add(b(u-j, o+j-1), j=1..u)+
add(expand(b(u+j-1, o-j)*x^(j-1)), j=1..o))
end:
a:= n-> coeff(b(n, 0), x, n):
seq(a(n), n=0..30);
MATHEMATICA
b[u_, o_] := b[u, o] = If[u + o == 0, 1, Sum[b[u - j, o + j - 1], {j, 1, u}] + Sum[Expand[b[u + j - 1, o - j]*x^(j - 1)], {j, 1, o}]];
a[n_] := Coefficient[b[n, 0], x, n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Dec 06 2023, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 31 2017
STATUS
approved