A179438 Number of rooted trees which can be associated with each unrestricted partition.

1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 1, 9, 4, 2, 2, 1, 1, 1, 20, 9, 4, 3

Offset

1,4

Comments

Values can be calculated using simple multiplication when all the parts of a partition are unequal; however when two or more parts are equal avoid over counting by adjusting as illustrated in the example.

References

N. L. Biggs, E. K. Lloyd and R. J. Wilson, Graph Theory 1736-1936, Clarendon Press, 1976, pages 40-43.

Links

Table of n, a(n) for n=1..22.

Example

Row six of the table begins:
20 9 4 3 ...
because the partitions begin:
6 5+1 4+2 3+3 ...
and A000081 begins 1,1,2,4,9,20,...
the partition 3+3 has two equal terms so we write
2*(2+1)/2! = 3.
Likewise, 3+3+3 has three equal terms so the expression becomes
2*(2+1)*(2+2)/3!

Crossrefs

Cf. A000041 (shape sequence) A000081 (row sums) A144963 (a related triangle)

Sequence in context: A365582 A367559 A099020 * A211970 A089688 A229706

Adjacent sequences: A179435 A179436 A179437 * A179439 A179440 A179441

Keyword

nonn,tabf,uned

Author

Alford Arnold, Jul 14 2010

Status

approved