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A261856
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.
2
31, 1305, 4955, 26765, 124450, 2008546, 4399870, 17016950, 51516925, 187653115, 2298210803, 4405690315, 14002637160, 37448507530, 109070884580, 308549728478, 3711879979775, 6377942356265, 19056675979455, 45667548869495, 122550455798230, 293681447602030
OFFSET
5,1
COMMENTS
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.
LINKS
FORMULA
a(n) = A261836(n,5).
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))(5):
seq(a(n), n=5..30);
CROSSREFS
Column k=5 of A261836.
Sequence in context: A182784 A139162 A078961 * A049292 A289473 A069406
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 03 2015
STATUS
approved