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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.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 03 2015
STATUS
approved