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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. 2
1, 1, 41, 8020, 4396189, 5226876501, 11581358373398, 43225961160925257, 252807246693691825421, 2194141947654736889023357, 27084992620572948369385642201, 459597167193175440533390098112664, 10424556988338412210154331381461375830 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

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-Fran├žois Alcover, Dec 14 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A322670.

Sequence in context: A221377 A160477 A221344 * A199652 A241111 A198713

Adjacent sequences:  A325478 A325479 A325480 * A325482 A325483 A325484

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 06 2019

STATUS

approved

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Last modified May 26 13:17 EDT 2022. Contains 354092 sequences. (Running on oeis4.)