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A261801

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

1, 9, 126, 1704, 22986, 310086, 4183260, 56435004, 761346207, 10271072557, 138563678736, 1869317246556, 25218347263608, 340212470558832, 4589695110222504, 61918074814238448, 835316485437693186, 11268981358631127288, 152026139882340589466

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OFFSET

0,2

COMMENTS

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.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..880

Index entries for linear recurrences with constant coefficients, signature (18, -72, 168, -252, 252, -168, 72, -18, 2).

FORMULA

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

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

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

MAPLE

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

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

end:

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