A261856 - OEIS

%I #4 Sep 03 2015 14:31:20

%S 31,1305,4955,26765,124450,2008546,4399870,17016950,51516925,

%T 187653115,2298210803,4405690315,14002637160,37448507530,109070884580,

%U 308549728478,3711879979775,6377942356265,19056675979455,45667548869495,122550455798230,293681447602030

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

%C Also number of matrices with five 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="/A261856/b261856.txt">Table of n, a(n) for n = 5..2500</a>

%F a(n) = A261836(n,5).

%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))(5):

%p seq(a(n), n=5..30);

%Y Column k=5 of A261836.

%K nonn

%O 5,1

%A _Alois P. Heinz_, Sep 03 2015