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

0,2

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);

Crossrefs

Column k=9 of A261780.

Sequence in context: A261743 A229283 A144073 * A065086 A246238 A234573

Adjacent sequences: A261798 A261799 A261800 * A261802 A261803 A261804

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 01 2015

Status

approved