A261857 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a senary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.

403, 3090, 26523, 178456, 4328268, 11655792, 55380132, 203857488, 908020203, 15089942326, 32659354659, 119798424120, 366557119686, 1229877368940, 4069268482608, 64750089252368, 122070519766665, 408439013722194, 1090232738714433, 3275624230408044

Offset

6,1

Comments

Also number of matrices with six rows of nonnegative integer entries and without zero rows or columns such that the sum of all entries is equal to n and the column sums are distinct.

Links

Alois P. Heinz, Table of n, a(n) for n = 6..2500

Formula

a(n) = A261836(n,6).

Maple

b:= proc(n, i, p, k) option remember;
      `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p, k)+
      `if`(i>n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
    end:
a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(6):
seq(a(n), n=6..30);

Crossrefs

Column k=6 of A261836.

Sequence in context: A213605 A083815 A250893 * A165808 A283662 A097741

Adjacent sequences: A261854 A261855 A261856 * A261858 A261859 A261860

Keyword

nonn

Author

Alois P. Heinz, Sep 03 2015

Status

approved