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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-François 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.)