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Search: id:A144293
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| 1, 1, 2, 5, 5, 13, 29, 877, 23, 53, 4639, 22619, 2423, 27644437, 1800937, 1101959, 43486067, 255755771, 5006399, 222527, 4326209287, 188633, 574631, 13369534669, 1204457631577, 171659, 11759883224809, 2479031, 171572636187431, 3516743833
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Contribution from David Pasino (davpas(AT)charter.net), Dec 03 2008: (Start)
The number of refinements of a partition is the product of the Bell numbers of the cell sizes.
The number of encoarsements is the Bell number of the number of cells.
For these to be equal, a Bell number has to be a product of Bell numbers.
This happens if there are n-1 single-element cells and 1 n-element cell.
Does it ever happen otherwise? (End)
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..70
Simon Plouffe, Factors of Bell numbers [From David Pasino (davpas(AT)charter.net), Dec 03 2008]
Author?, rime number checker up to 10000000000 [From David Pasino (davpas(AT)charter.net), Dec 03 2008]
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CROSSREFS
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Adjacent sequences: A144290 A144291 A144292 this_sequence A144294 A144295 A144296
Sequence in context: A100953 A112835 A154692 this_sequence A154694 A154696 A154698
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 03 2008
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EXTENSIONS
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a(15) - a(20) from David Pasino (davpas(AT)charter.net), Dec 03 2008
a(21) onwards from N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2008
Corrected by David Pasino (davpas(AT)charter.net), Dec 14 2008
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