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A179438
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Number of rooted trees which can be associated with each unrestricted partition.
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1
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1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 1, 9, 4, 2, 2, 1, 1, 1, 20, 9, 4, 3
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OFFSET
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1,4
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COMMENTS
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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.
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REFERENCES
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N. L. Biggs, E. K. Lloyd and R. J. Wilson, Graph Theory 1736-1936, Clarendon Press, 1976, pages 40-43.
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LINKS
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Table of n, a(n) for n=1..22.
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EXAMPLE
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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!
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CROSSREFS
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Cf. A000041 (shape sequence) A000081 (row sums) A144963 (a related triangle)
Sequence in context: A021477 A124939 A099020 * A211970 A089688 A092479
Adjacent sequences: A179435 A179436 A179437 * A179439 A179440 A179441
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KEYWORD
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nonn,tabf,uned,changed
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AUTHOR
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Alford Arnold, Jul 14 2010
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STATUS
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approved
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