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 A325890 Number of colored set partitions of [n] where colors of the elements of subsets are in (weakly) increasing order and exactly two colors are used. 2
 3, 20, 122, 774, 5247, 38198, 298139, 2485690, 22045130, 207125874, 2053771931, 21416863948, 234145149539, 2676207794512, 31898152797430, 395584489687982, 5093960430643323, 67985187315217290, 938835976835478467, 13394336734762313862, 197153821757472332126 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 2..535 MAPLE b:= proc(n, k) option remember; `if`(n=0, 1, add(b(n-j, k)* binomial(n-1, j-1)*binomial(k+j-1, j), j=1..n)) end: a:= n-> (k-> add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(2): seq(a(n), n=2..25); MATHEMATICA b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - j, k] Binomial[n - 1, j - 1] Binomial[k + j - 1, j], {j, 1, n}]]; a[n_] := With[{k = 2}, Sum[b[n, k - i] (-1)^i Binomial[k, i], {i, 0, k}]]; a /@ Range[2, 25] (* Jean-François Alcover, Dec 15 2020, after Alois P. Heinz *) CROSSREFS Column k=2 of A321296. Sequence in context: A228066 A009125 A037795 * A323563 A228750 A187442 Adjacent sequences: A325887 A325888 A325889 * A325891 A325892 A325893 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 07 2019 STATUS approved

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Last modified September 7 20:21 EDT 2024. Contains 375749 sequences. (Running on oeis4.)