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A261859
Number of compositions of n into distinct parts where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
2
2873, 66904, 4351388, 20331080, 157483354, 901563512, 6174438308, 180660353288, 511805155863, 2507827775824, 10089884785056, 44796664928048, 200977872433624, 5149800722642960, 11741438872834432, 48645418597510928, 159659060979170671, 593940633500376248
OFFSET
8,1
COMMENTS
Also number of matrices with eight 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,8).
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))(8):
seq(a(n), n=8..30);
CROSSREFS
Column k=8 of A261836.
Sequence in context: A254587 A254580 A254355 * A286526 A081427 A101999
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 03 2015
STATUS
approved