A261802 Number of 10-compositions of n: matrices with 10 rows of nonnegative integers with positive column sums and total element sum n.

1, 10, 155, 2320, 34640, 517252, 7723970, 115339960, 1722340115, 25719233330, 384058268507, 5735036957760, 85639736481880, 1278834734405320, 19096488909285540, 285162639746429024, 4258255614078447290, 63587365059302801520, 949532710487622388080

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 denary alphabet whose letters appear in alphabetical order.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..850

Formula

G.f.: (1-x)^10/(2*(1-x)^10-1).

a(n) = A261780(n,10).

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-j)*binomial(j+9, 9), j=1..n))
    end:
seq(a(n), n=0..20);

Crossrefs

Column k=10 of A261780.

Sequence in context: A229284 A087603 A292837 * A246239 A235340 A306034

Adjacent sequences: A261799 A261800 A261801 * A261803 A261804 A261805

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 01 2015

Status

approved