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A327768 Number of colored compositions of n using all colors of a 2-set such that all parts have different color patterns and the patterns for parts i are sorted and have i colors (in arbitrary order). 2
0, 0, 3, 18, 60, 210, 798, 2462, 7891, 25148, 84173, 257558, 810924, 2515962, 7706020, 24261554, 73746402, 224417982, 683672754, 2057559942, 6177146990, 18671429714, 55589344618, 165403412230, 491940143015, 1452537550800, 4280665171599, 12578264746522 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..800

EXAMPLE

a(2) = 3: 2ab, 2ba, 1a1b.

a(3) = 18: 3aab, 3aba, 3baa, 3abb, 3bab, 3bba, 2aa1b, 2ab1a, 2ba1a, 2ab1b, 2ba1b, 2bb1a, 1a2ab, 1a2ba, 1a2bb, 1b2aa, 1b2ab, 1b2ba.

MAPLE

b:= proc(n, i, k, p) option remember;

     `if`(n=0, p!, `if`(i<1, 0, add(binomial(k^i, j)*

      b(n-i*j, min(n-i*j, i-1), k, p+j)/j!, j=0..n/i)))

    end:

a:= n-> (k-> add(b(n$2, i, 0)*(-1)^(k-i)*binomial(k, i), i=0..k))(2):

seq(a(n), n=0..27);

CROSSREFS

Column k=2 of A327673.

Sequence in context: A012763 A006011 A012779 * A074439 A299031 A210366

Adjacent sequences:  A327765 A327766 A327767 * A327769 A327770 A327771

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 24 2019

STATUS

approved

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Last modified May 9 00:09 EDT 2021. Contains 343685 sequences. (Running on oeis4.)