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A261860 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a nonary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition. 2

%I #4 Sep 03 2015 17:36:56

%S 12607,1850013,13188465,141059073,1056825045,9244127655,358616974839,

%T 1185100976313,6776480736882,31512728488918,161603593094034,

%U 844675656403032,26805281002135578,67485379090772970,310715577607315770,1129828504295753862,4665897718158585321

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

%C Also number of matrices with nine 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="/A261860/b261860.txt">Table of n, a(n) for n = 9..2000</a>

%F a(n) = A261836(n,9).

%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))(9):

%p seq(a(n), n=9..30);

%Y Column k=9 of A261836.

%K nonn

%O 9,1

%A _Alois P. Heinz_, Sep 03 2015

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)