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

Author

Alford Arnold, Jul 14 2010

Keywords

• nonn
• tabf
• uned

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.

Examples

			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!
		

References

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

Crossrefs

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