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Search: id:A086659
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| A086659 |
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T(n,k) counts the set partitions of n containing k-1 blocks of length 1. |
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+0
3
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| 1, 1, 3, 4, 4, 6, 11, 20, 10, 10, 41, 66, 60, 20, 15, 162, 287, 231, 140, 35, 21, 715, 1296, 1148, 616, 280, 56, 28, 3425, 6435, 5832, 3444, 1386, 504, 84, 36, 17722, 34250, 32175, 19440, 8610, 2772, 840, 120, 45, 98253, 194942, 188375, 117975, 53460
(list; table; graph; listen)
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OFFSET
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2,3
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FORMULA
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E.g.f.: exp(x*y)*(exp(exp(x)-1-x)-1). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 28 2003
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EXAMPLE
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The 15 set partitions of {1,2,3,4} consist of 4 partitions with 0 blocks of length 1 : {{1,2,3,4}},{{1,2},{3,4}},{{1,3},{2,4}},{{1,4},{2,3}},
4 partitions with 1 block of length 1 : {{1},{2,3,4}},{{1,2,3},{4}},{{1,2,4},{3}},{{1,3,4},{2}}
6 partitions with 2 blocks of length 1 : {{1},{2},{3,4}},{{1},{2,3},{4}},{{1},{2,4},{3}},{{1,2},{3},{4}},{{1,3},{2},{4}},{{1,4},{2},{3}}.
(There are no partitions with n-1 blocks of length 1, and 1 with n of them)
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MATHEMATICA
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Table[Count[Count[ #, {_Integer}]&/@SetPartitions[n], # ]&/@Range[0, n-2], {n, 2, 10}]
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CROSSREFS
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Row sums = Bell[n]-1 (A058692), first column=A000296, main diagonal = triangular numbers A000217.
Adjacent sequences: A086656 A086657 A086658 this_sequence A086660 A086661 A086662
Sequence in context: A047877 A100692 A089640 this_sequence A008473 A069088 A019462
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jul 27 2003
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 28 2003
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