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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.
2

%I #4 Sep 03 2015 08:36:50

%S 1,9,45,975,3465,25047,471669,1542519,8361540,43916950,934748298,

%T 2560160538,12924414750,52656337800,271075650210,5853558884496,

%U 14764118156523,65116959410547,241547985000289,1004388404964615,4276652360222781,104392134731727315

%N 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.

%C Also matrices with two nine of nonnegative integers with distinct positive column sums and total element sum n.

%H Alois P. Heinz, <a href="/A261847/b261847.txt">Table of n, a(n) for n = 0..4921</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+8, 8))))

%p end:

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

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

%Y Column k=9 of A261835.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Sep 03 2015