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Search: id:A144979
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| A144979 |
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Number of hyperforests on n unlabeled nodes, assuming that each edge contains at least two nodes, with all components of prime orders. |
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+0
1
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| 0, 1, 2, 3, 11, 15, 70, 92, 166, 351, 5061, 5782, 60736, 73183, 135152, 303426, 8507114, 9468630, 119603007, 140712654, 262160102, 593434948, 21042972101, 23146479248, 44736887989, 96738104613, 122459045525
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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D. E. Knuth: The Art of Computer Programming, Volume 4, Generating All Combinations and Partitions Fascicle 3, Section 7.2.1.4. Generating all partitions. Page 38, Algorithm H.
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LINKS
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W. Bomfim, A picture of the Hindenburg's Partition Generator
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FORMULA
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a(n) = Sum of prod_{k=1}^n\,{A035053(k) + c_k -1 /choose c_k} over the partitions of n having all parts k prime, c_1 + 2c_2 + ... + nc_n; c_1, c_2, ..., c_n >= 0.
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EXAMPLE
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a(5) = 11 since the only options are 9 hypertrees of order 5, or the two hyperforests composed by components of order 3 and 2.
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CROSSREFS
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Cr A035053(hypertrees), A000040(prime numbers).
Sequence in context: A042235 A050587 A066687 this_sequence A076514 A071012 A091734
Adjacent sequences: A144976 A144977 A144978 this_sequence A144980 A144981 A144982
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KEYWORD
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nonn
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AUTHOR
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W. Bomfim (webonfim(AT)bol.com.br), Sep 28 2008
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