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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.
3
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 03 2015
STATUS
approved