cp's OEIS Frontend

A261859 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.

%I A261859 #4 Sep 03 2015 17:28:50
%S A261859 2873,66904,4351388,20331080,157483354,901563512,6174438308,
%T A261859 180660353288,511805155863,2507827775824,10089884785056,
%U A261859 44796664928048,200977872433624,5149800722642960,11741438872834432,48645418597510928,159659060979170671,593940633500376248
%N A261859 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 A261859 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 A261859 Alois P. Heinz, <a href="/A261859/b261859.txt">Table of n, a(n) for n = 8..2000</a>
%F A261859 a(n) = A261836(n,8).
%p A261859 b:= proc(n, i, p, k) option remember;
%p A261859       `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p, k)+
%p A261859       `if`(i>n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
%p A261859     end:
%p A261859 a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(8):
%p A261859 seq(a(n), n=8..30);
%Y A261859 Column k=8 of A261836.
%K A261859 nonn
%O A261859 8,1
%A A261859 _Alois P. Heinz_, Sep 03 2015