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A261856
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Number of compositions of n into distinct parts where each part i is marked with a word of length i over a quinary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
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2
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31, 1305, 4955, 26765, 124450, 2008546, 4399870, 17016950, 51516925, 187653115, 2298210803, 4405690315, 14002637160, 37448507530, 109070884580, 308549728478, 3711879979775, 6377942356265, 19056675979455, 45667548869495, 122550455798230, 293681447602030
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OFFSET
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5,1
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COMMENTS
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Also number of matrices with five 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.
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LINKS
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FORMULA
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MAPLE
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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))(5):
seq(a(n), n=5..30);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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