A327847 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 have i colors in (weakly) increasing order.

0, 0, 3, 10, 39, 100, 303, 782, 2009, 5388, 12839, 32658, 79673, 191500, 459745, 1090622, 2569597, 5932304, 13906405, 31740090, 72160311, 164296384, 369673125, 827781598, 1834885695, 4076433368, 8966677703, 19639987986, 42751905899, 92703023676, 200647122467

Offset: 0

Author

Alois P. Heinz, Sep 27 2019

Keywords

• nonn

Examples

			a(3) = 10: 3aab, 3abb, 2aa1b, 2ab1a, 2ab1b, 2bb1a, 1a2ab, 1a2bb, 1b2aa, 1b2ab.
		

Links

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

Crossrefs

Column k=2 of A327245.

Programs

Maple

b:= proc(n, i, k, p) option remember; `if`(n=0, p!,
     `if`(i<1, 0, add(b(n-i*j, min(n-i*j, i-1), k, p+j)*
      binomial(binomial(k+i-1, i), 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..37);