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Search: id:A105481
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| A105481 |
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Number of partitions of {1...n} containing 4 pairs of consecutive integers, where each pair is counted within a block and a string of more that 2 consecutive integers are counted two at a time. |
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5
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| 1, 5, 30, 175, 1050, 6552, 42630, 289410, 2049300, 15120105, 116090975, 926248050, 7668746540, 65793760060, 584151925320, 5360347320420, 50776288702215, 495946245776940, 4989391837053085, 51648932225779735, 549620905409062872
(list; graph; listen)
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OFFSET
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5,2
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REFERENCES
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A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451-463.
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LINKS
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A. O. Munagi, Set Partitions with Successions and Separations,IJMMS 2005:3 (2005),451-463.
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FORMULA
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a(n) = binomial(n-1, 4)Bell(n-5), the case r = 4 in the general case of r pairs: c(n, r) = binomial(n-1, r)B(n-r-1).
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EXAMPLE
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a(6) = 5 because the partitions of {1,2,3,4,5,6} with 4 pairs of consecutive integers are 12345/6,1234/56,123/456,12/3456,1/23456.
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MAPLE
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seq(binomial(n-1, 4)*combinat[bell](n-5), n=5..25);
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CROSSREFS
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Cf. A105480, A105482, A105486, A105491, A105494.
Sequence in context: A084158 A111469 A057088 this_sequence A051738 A094167 A052934
Adjacent sequences: A105478 A105479 A105480 this_sequence A105482 A105483 A105484
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KEYWORD
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easy,nonn
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AUTHOR
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A. O. Munagi (amunagi(AT)yahoo.com), Apr 10 2005
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