1,2

In other words, it shows how many partitions of n have k different partitions of n+1 just covering it.

As an irregular triangle:

1

3

3 3

6 6 0 1

3 15 3 3

9 21 6 12

3 34 21 25 3

10 45 36 54 15

6 54 72 108 36 6

As a table:

k:=1 k:=2 k:=3 k:=4 k:=5 k:=6 k:=7 k:=8 k:=9 k:=10 k:=11 k:=12

n:=1 0 0 1 0 0 0 0 0 0 0 0 0

n:=2 0 0 3 0 0 0 0 0 0 0 0 0

n:=3 0 0 3 3 0 0 0 0 0 0 0 0

n:=4 0 0 6 6 0 1 0 0 0 0 0 0

n:=5 0 0 3 15 3 3 0 0 0 0 0 0

n:=6 0 0 9 21 6 12 0 0 0 0 0 0

n:=7 0 0 3 34 21 25 3 0 0 0 0 0

n:=8 0 0 10 45 36 54 15 0 0 0 0 0

n:=9 0 0 6 54 72 108 36 6 0 0 0 0

Row sums are A000219; the weighted products (dot product with the k's) is A090984.

Sequence in context: A100049 A158315 A134059 this_sequence A098529 A133774 A108581

Adjacent sequences: A112666 A112667 A112668 this_sequence A112670 A112671 A112672

nonn,tabf

Wouter Meeussen (wouter.meeussen(AT)pandora.be), Sep 07 2004