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A102356
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Problem 65 in Knuth's Art of Computer Programming, vol. 4, section 7.2.1.5 asks which integer partition of n produces the most set partitions. The n-th term of this sequence is the number of set partitions produced by that integer partition.
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4
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1, 1, 1, 3, 6, 15, 60, 210, 840, 3780, 12600, 69300, 415800, 2702700, 12612600, 94594500, 756756000, 4288284000, 38594556000, 244432188000, 1833241410000, 17110253160000, 141159588570000, 1298668214844000, 10389345718752000, 108222351237000000, 1125512452864800000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n) is the maximum value in row n of A080575.
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LINKS
| D. E. Knuth, The Art of Computer Programming, vol. 4
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EXAMPLE
| a(4) = 6 because there are 6 set partitions of type {2,1,1}, namely 12/3/4, 13/2/4, 1/23/4, 14/2/3, 1/24/3, 1/2/34; all other integer partitions of 4 produce fewer set partitions.
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MATHEMATICA
| sp[l_] := (Total[l])!/(Apply[Times, Map[ #! &, l]]*Apply[Times, Map[Count[l, # ]! &, Range[Max[l]]]]) a[n_] := Max[Map[sp, Partitions[n]]]
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CROSSREFS
| Cf. A080575.
Sequence in context: A005655 A051169 A051610 * A102936 A009192 A013273
Adjacent sequences: A102353 A102354 A102355 * A102357 A102358 A102359
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KEYWORD
| nonn
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AUTHOR
| Dan Drake (drake(AT)math.umn.edu), Feb 21 2005
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EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 13 2011
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