A261801 - OEIS

%I #16 Aug 21 2024 09:43:10

%S 1,9,126,1704,22986,310086,4183260,56435004,761346207,10271072557,

%T 138563678736,1869317246556,25218347263608,340212470558832,

%U 4589695110222504,61918074814238448,835316485437693186,11268981358631127288,152026139882340589466

%N Number of 9-compositions of n: matrices with 9 rows of nonnegative integers with positive column sums and total element sum n.

%C Also the number of compositions of n where each part i is marked with a word of length i over a nonary alphabet whose letters appear in alphabetical order.

%H Alois P. Heinz, <a href="/A261801/b261801.txt">Table of n, a(n) for n = 0..880</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (18, -72, 168, -252, 252, -168, 72, -18, 2).

%F G.f.: (1-x)^9/(2*(1-x)^9-1).

%F a(n) = A261780(n,9).

%F a(n) = Sum_{k>=0} (1/2)^(k+1) * binomial(n-1+9*k,n). - _Seiichi Manyama_, Aug 06 2024

%p a:= proc(n) option remember; `if`(n=0, 1,

%p       add(a(n-j)*binomial(j+8, 8), j=1..n))

%p     end:

%p seq(a(n), n=0..20);

%Y Column k=9 of A261780.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Sep 01 2015