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%I #4 Sep 03 2015 15:47:50
%S 757,13671,148638,5623044,19334910,115231480,522931570,2868333476,
%T 63481817735,156363633615,661651830728,2317522429544,8940138012274,
%U 34465610055870,703252581037436,1456494080466446,5428978793488341,16082092961535517,53836540488601696
%N 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.
%C 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.
%H Alois P. Heinz, <a href="/A261858/b261858.txt">Table of n, a(n) for n = 7..2500</a>
%F a(n) = A261836(n,7).
%p b:= proc(n, i, p, k) option remember;
%p `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p, k)+
%p `if`(i>n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
%p end:
%p a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(7):
%p seq(a(n), n=7..30);
%Y Column k=7 of A261836.
%K nonn
%O 7,1
%A _Alois P. Heinz_, Sep 03 2015
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