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Search: id:A105491
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| A105491 |
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Number of partitions of {1...n} containing 5 detached pairs of consecutive integers, i.e., partitions in which only 1- or 2-strings of consecutive integers can appear in a block and there are exactly five 2-strings. |
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4
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| 15, 312, 4263, 49112, 521640, 5329044, 53580450, 537427440, 5422899339, 55344162874, 573270663966, 6040762924560, 64851119605636, 709986204480672, 7931189102016852, 90430835147203728, 1052534895931584828
(list; graph; listen)
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OFFSET
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10,1
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COMMENT
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Number of partitions enumerated by A105482 in which the maximal length of consecutive integers in a block is 2.
With offset 5t, number of partitions of {1,...,N} containing 5 detached strings of t consecutive integers, where N=n+5j, t=2+j, j = 0,1,2,..., i.e., partitions of {1,...,N} in which only v-strings of consecutive integers can appear in a block, where v=1 or v=t and there are exactly five t-strings.
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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-5, 5)*Bell(n-6), which is the case r=5 in the general case of r pairs, d(n, r)=binomial(n-r, r)*Bell(n-r-1), which is the case t=2 of the general formula d(n, r, t)=binomial(n-r*(t-1), r)*B(n-r*(t-1)-1).
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EXAMPLE
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a(10)=15; the enumerated 15 partitions of {1,...,10} with 5 detached pairs of consecutive integers include (1,2,5,6,9,10)(3,4,7,8) and (1,2,9,10)(3,4,7,8)(5,6).
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MAPLE
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seq(binomial(n-5, 5)*combinat[bell](n-6), n=10..30);
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CROSSREFS
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Cf. A105482, A105490, A105487.
Adjacent sequences: A105488 A105489 A105490 this_sequence A105492 A105493 A105494
Sequence in context: A049381 A051691 A135390 this_sequence A133766 A112489 A062757
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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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