A261858 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a septenary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.

757, 13671, 148638, 5623044, 19334910, 115231480, 522931570, 2868333476, 63481817735, 156363633615, 661651830728, 2317522429544, 8940138012274, 34465610055870, 703252581037436, 1456494080466446, 5428978793488341, 16082092961535517, 53836540488601696

Offset

7,1

Comments

Also number of matrices with seven 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 = 7..2500

Formula

a(n) = A261836(n,7).

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))(7):
seq(a(n), n=7..30);

Crossrefs

Column k=7 of A261836.

Sequence in context: A291864 A173507 A101833 * A068683 A221340 A290738

Adjacent sequences: A261855 A261856 A261857 * A261859 A261860 A261861

Keyword

nonn

Author

Alois P. Heinz, Sep 03 2015

Status

approved