cp's OEIS Frontend

A261848 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.

%I A261848 #4 Sep 03 2015 09:38:29
%S A261848 1,10,55,1320,5115,40502,849695,3005860,17729140,101710180,2427338628,
%T A261848 7149947740,39019448520,172243529680,967216439310,23628910183516,
%U A261848 63666698290635,302259439194130,1206608816442095,5423457474305640,25200103664372021,701550193438735410
%N A261848 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.
%C A261848 Also matrices with ten rows of nonnegative integers with distinct positive column sums and total element sum n.
%H A261848 Alois P. Heinz, <a href="/A261848/b261848.txt">Table of n, a(n) for n = 0..4430</a>
%p A261848 b:= proc(n, i, p) option remember;
%p A261848       `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p)+
%p A261848       `if`(i>n, 0, b(n-i, i-1, p+1)*binomial(i+9, 9))))
%p A261848     end:
%p A261848 a:= n-> b(n$2, 0):
%p A261848 seq(a(n), n=0..25);
%Y A261848 Column k=10 of A261835.
%K A261848 nonn
%O A261848 0,2
%A A261848 _Alois P. Heinz_, Sep 03 2015