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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 denary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
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%I #4 Sep 03 2015 17:44:48

%S 333051,4822430,79871395,832560780,9644631215,503145835150,

%T 1977105518235,13353202808060,72444344358890,431802346970780,

%U 2638310862477610,102808411342614000,286995037461236030,1470656290936993540,5931973064021096010,27203387338778029760

%N Number of compositions of n into distinct parts where each part i is marked with a word of length i over a denary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.

%C Also number of matrices with ten 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="/A261861/b261861.txt">Table of n, a(n) for n = 10..2000</a>

%F a(n) = A261836(n,10).

%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))(10):

%p seq(a(n), n=10..30);

%Y Column k=10 of A261836.

%K nonn

%O 10,1

%A _Alois P. Heinz_, Sep 03 2015