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).

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

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