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A332244
Number of chains of length n in the lattice of set partitions of [2n] ordered by refinement.
2
1, 2, 45, 8176, 5967927, 12354550875, 58745934381618, 557269710685272585, 9536970947556120868800, 273107814151944184186060560, 12345107536247705318429028256740, 840776466106445249176017830108333910, 83061829400676435859326576547506817501212
OFFSET
0,2
LINKS
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: A374863 A209606 A100101 * A090601 A266016 A071777
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 07 2020
STATUS
approved