cp's OEIS Frontend

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.

%I A261860 #4 Sep 03 2015 17:36:56
%S A261860 12607,1850013,13188465,141059073,1056825045,9244127655,358616974839,
%T A261860 1185100976313,6776480736882,31512728488918,161603593094034,
%U A261860 844675656403032,26805281002135578,67485379090772970,310715577607315770,1129828504295753862,4665897718158585321
%N 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.
%C A261860 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 A261860 Alois P. Heinz, <a href="/A261860/b261860.txt">Table of n, a(n) for n = 9..2000</a>
%F A261860 a(n) = A261836(n,9).
%p A261860 b:= proc(n, i, p, k) option remember;
%p A261860       `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p, k)+
%p A261860       `if`(i>n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
%p A261860     end:
%p A261860 a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(9):
%p A261860 seq(a(n), n=9..30);
%Y A261860 Column k=9 of A261836.
%K A261860 nonn
%O A261860 9,1
%A A261860 _Alois P. Heinz_, Sep 03 2015