A327841 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 (weakly) increasing order.

0, 0, 2, 10, 27, 70, 223, 508, 1193, 2822, 7048, 15690, 35072, 79018, 167667, 382976, 823599, 1742082, 3765187, 7785290, 16299074, 34337380, 70503188, 143916326, 296390373, 597048414, 1202172962, 2416614660, 4813022691, 9551780272, 18833189269, 37248671816

Offset: 0

Author

Alois P. Heinz, Sep 27 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=2 of A327244.

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)/
       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..35);