A261848 - OEIS

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 #4 Sep 03 2015 09:38:29

%S 1,10,55,1320,5115,40502,849695,3005860,17729140,101710180,2427338628,

%T 7149947740,39019448520,172243529680,967216439310,23628910183516,

%U 63666698290635,302259439194130,1206608816442095,5423457474305640,25200103664372021,701550193438735410

%N 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 Also matrices with ten rows of nonnegative integers with distinct positive column sums and total element sum n.

%H Alois P. Heinz, <a href="/A261848/b261848.txt">Table of n, a(n) for n = 0..4430</a>

%p b:= proc(n, i, p) option remember;

%p `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p)+

%p `if`(i>n, 0, b(n-i, i-1, p+1)*binomial(i+9, 9))))

%p end:

%p a:= n-> b(n$2, 0):

%p seq(a(n), n=0..25);

%Y Column k=10 of A261835.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Sep 03 2015