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 A327890 Number of colored integer partitions of n using all colors of a 2-set such that parts i have distinct color patterns in arbitrary order and each pattern for a part i has i colors in (weakly) increasing order. 2
 0, 0, 3, 6, 21, 42, 90, 176, 348, 640, 1203, 2152, 3848, 6692, 11701, 19968, 33966, 56952, 95300, 157326, 258736, 421240, 683804, 1099830, 1762867, 2805154, 4446826, 7005486, 10999634, 17172894, 26716627, 41362952, 63837722, 98079482, 150216194, 229155682 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..4000 (terms 0..1000 from Alois P. Heinz) EXAMPLE a(3) = 6: 3aab, 3abb, 2aa1b, 2ab1a, 2ab1b, 2bb1a. MAPLE b:= proc(n, i, k) option remember; `if`(n=0, 1,       `if`(i<1, 0, add(b(n-i*j, min(n-i*j, i-1), k)*        binomial(binomial(k+i-1, i), j)*j!, j=0..n/i)))     end: a:= n-> (k-> add(b(n\$2, i)*(-1)^(k-i)*binomial(k, i), i=0..k))(2): seq(a(n), n=0..44); MATHEMATICA b[n_, i_, k_] := b[n, i, k] = If[n==0, 1, If[i<1, 0, Sum[b[n - i*j, Min[n - i*j, i-1], k] Binomial[Binomial[k+i-1, i], j] j!, {j, 0, n/i}]]]; a[n_] := With[{k = 2}, Sum[b[n, n, i](-1)^(k-i)Binomial[k, i], {i, 0, k}]]; a /@ Range[0, 44] (* Jean-François Alcover, Dec 18 2020, after Alois P. Heinz *) CROSSREFS Column k=2 of A309973. Sequence in context: A056489 A015649 A297189 * A076102 A094282 A124493 Adjacent sequences:  A327887 A327888 A327889 * A327891 A327892 A327893 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 29 2019 STATUS approved

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Last modified April 22 22:19 EDT 2021. Contains 343197 sequences. (Running on oeis4.)