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

0,3

Links

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

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);

Crossrefs

Column k=2 of A327244.

Sequence in context: A328743 A133479 A196324 * A196648 A220700 A057753

Adjacent sequences: A327838 A327839 A327840 * A327842 A327843 A327844

Keyword

nonn

Author

Alois P. Heinz, Sep 27 2019

Status

approved