A261859 - OEIS

%I #4 Sep 03 2015 17:28:50

%S 2873,66904,4351388,20331080,157483354,901563512,6174438308,

%T 180660353288,511805155863,2507827775824,10089884785056,

%U 44796664928048,200977872433624,5149800722642960,11741438872834432,48645418597510928,159659060979170671,593940633500376248

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

%C Also number of matrices with eight 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="/A261859/b261859.txt">Table of n, a(n) for n = 8..2000</a>

%F a(n) = A261836(n,8).

%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))(8):

%p seq(a(n), n=8..30);

%Y Column k=8 of A261836.

%K nonn

%O 8,1

%A _Alois P. Heinz_, Sep 03 2015