OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..133
Wikipedia, Lattice (order)
Wikipedia, Partition of a set
FORMULA
a(n) = A331955(2n,n).
MAPLE
b:= proc(n, k, t) option remember; `if`(k<0, 0, `if`({n, k}={0}, 1,
add(`if`(k=1, 1, b(v, k-1, 1))*Stirling2(n, v), v=k..n-t)))
end:
a:= n-> b(2*n, n, 0):
seq(a(n), n=0..14);
MATHEMATICA
b[n_, k_, t_] := b[n, k, t] = If[k < 0, 0, If[Union@{n, k} == {0}, 1, Sum[ If[k == 1, 1, b[v, k - 1, 1]] StirlingS2[n, v], {v, k, n - t}]]];
a[n_] := b[2n, n, 0];
a /@ Range[0, 14] (* Jean-François Alcover, May 08 2020, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 07 2020
STATUS
approved