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

Offset: 0

Author

Alois P. Heinz, Sep 01 2015

Keywords

• nonn
• easy

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).

Crossrefs

Column k=9 of A261780.

Programs

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);

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