cp's OEIS Frontend

A261857 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a senary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.

%I A261857 #4 Sep 03 2015 14:48:59
%S A261857 403,3090,26523,178456,4328268,11655792,55380132,203857488,908020203,
%T A261857 15089942326,32659354659,119798424120,366557119686,1229877368940,
%U A261857 4069268482608,64750089252368,122070519766665,408439013722194,1090232738714433,3275624230408044
%N A261857 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a senary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
%C A261857 Also number of matrices with six 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 A261857 Alois P. Heinz, <a href="/A261857/b261857.txt">Table of n, a(n) for n = 6..2500</a>
%F A261857 a(n) = A261836(n,6).
%p A261857 b:= proc(n, i, p, k) option remember;
%p A261857       `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p, k)+
%p A261857       `if`(i>n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
%p A261857     end:
%p A261857 a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(6):
%p A261857 seq(a(n), n=6..30);
%Y A261857 Column k=6 of A261836.
%K A261857 nonn
%O A261857 6,1
%A A261857 _Alois P. Heinz_, Sep 03 2015