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A002846
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Number of ways of transforming a set of n indistinguishable objects into n singletons via a sequence of n-1 refinements.
(Formerly M1251 N0478)
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0
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1, 1, 1, 2, 4, 11, 33, 116, 435, 1832, 8167, 39700, 201785, 1099449, 6237505, 37406458, 232176847, 1513796040, 10162373172, 71158660160, 511957012509, 3819416719742, 29195604706757, 230713267586731, 1861978821637735
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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REFERENCES
| P. Erdos, R. K. Guy and J. W. Moon, On refining partitions, J. London Math. Soc., 9 (1975), 565-570.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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EXAMPLE
| a(5) = 4 because there are 4 paths from top to bottom in this lattice:
.....ooooo.......
.../......\......
o.oooo...oo.ooo..
..|....X....|....
o.o.ooo..o.oo.oo.
...\......./.....
....o.o.o.oo.....
........|........
....o.o.o.o.o....
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MATHEMATICA
| <<posets.m Table[Build[NumP[n], np]; Last@MaximalChainsDown@np, {n, 1, 25}] - (Harris)
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CROSSREFS
| Sequence in context: A192405 A035354 A127782 * A188478 A123444 A123473
Adjacent sequences: A002843 A002844 A002845 * A002847 A002848 A002849
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| a(17)-a(25) from Mitch Harris, Jan 19 2006
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