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A179438
Number of rooted trees which can be associated with each unrestricted partition.
1
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.
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
KEYWORD
nonn,tabf,uned
AUTHOR
Alford Arnold, Jul 14 2010
STATUS
approved