A325481 Number of colored set partitions of [2n] where colors of the elements of subsets are distinct and in increasing order and exactly n colors are used.

1, 1, 41, 8020, 4396189, 5226876501, 11581358373398, 43225961160925257, 252807246693691825421, 2194141947654736889023357, 27084992620572948369385642201, 459597167193175440533390098112664, 10424556988338412210154331381461375830

Offset: 0

Author

Alois P. Heinz, Sep 06 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..151

Crossrefs

Cf. A322670.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(b(n-j, k)*
      binomial(n-1, j-1)*binomial(k, j), j=1..min(k, n)))
    end:
a:= n-> add(b(2*n, n-i)*(-1)^i*binomial(n, i), i=0..n):
seq(a(n), n=0..14);

Mathematica

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - j, k] Binomial[n - 1, j - 1] Binomial[k, j], {j, 1, Min[k, n]}]];
a[n_] := Sum[b[2n, n - i] (-1)^i Binomial[n, i], {i, 0, n}];
a /@ Range[0, 14] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)

Formula

a(n) = A322670(2n,n).