A332244 Number of chains of length n in the lattice of set partitions of [2n] ordered by refinement.

1, 2, 45, 8176, 5967927, 12354550875, 58745934381618, 557269710685272585, 9536970947556120868800, 273107814151944184186060560, 12345107536247705318429028256740, 840776466106445249176017830108333910, 83061829400676435859326576547506817501212

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

Cf. A331955.

Sequence in context: A092654 A209606 A100101 * A090601 A266016 A071777

Adjacent sequences: A332241 A332242 A332243 * A332245 A332246 A332247

Keyword

nonn

Author

Alois P. Heinz, Feb 07 2020

Status

approved