cp's OEIS Frontend

A261861 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a denary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.

%I A261861 #4 Sep 03 2015 17:44:48
%S A261861 333051,4822430,79871395,832560780,9644631215,503145835150,
%T A261861 1977105518235,13353202808060,72444344358890,431802346970780,
%U A261861 2638310862477610,102808411342614000,286995037461236030,1470656290936993540,5931973064021096010,27203387338778029760
%N A261861 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a denary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
%C A261861 Also number of matrices with ten 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 A261861 Alois P. Heinz, <a href="/A261861/b261861.txt">Table of n, a(n) for n = 10..2000</a>
%F A261861 a(n) = A261836(n,10).
%p A261861 b:= proc(n, i, p, k) option remember;
%p A261861       `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p, k)+
%p A261861       `if`(i>n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
%p A261861     end:
%p A261861 a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(10):
%p A261861 seq(a(n), n=10..30);
%Y A261861 Column k=10 of A261836.
%K A261861 nonn
%O A261861 10,1
%A A261861 _Alois P. Heinz_, Sep 03 2015