cp's OEIS Frontend

A261843 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.

%I A261843 #4 Sep 03 2015 05:51:21
%S A261843 1,5,15,185,420,1876,19320,42610,149115,495205,5516001,10570145,
%T A261843 35897010,97383790,320607680,3412039628,6292069835,19106603405,
%U A261843 49239854095,138462457915,378598491878,4312038483490,7316190877970,21527078513430,50933081112485
%N A261843 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.
%C A261843 Also matrices with five rows of nonnegative integers with distinct positive column sums and total element sum n.
%H A261843 Alois P. Heinz, <a href="/A261843/b261843.txt">Table of n, a(n) for n = 0..5000</a>
%p A261843 b:= proc(n, i, p) option remember;
%p A261843       `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p)+
%p A261843       `if`(i>n, 0, b(n-i, i-1, p+1)*binomial(i+4, 4))))
%p A261843     end:
%p A261843 a:= n-> b(n$2, 0):
%p A261843 seq(a(n), n=0..30);
%Y A261843 Column k=5 of A261835.
%K A261843 nonn
%O A261843 0,2
%A A261843 _Alois P. Heinz_, Sep 03 2015