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A105490
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Number of partitions of {1...n} containing 4 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 four 2-strings.
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5
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5, 75, 780, 7105, 61390, 521640, 4440870, 38271750, 335892150, 3012721855, 27672081437, 260577574530, 2516984551900, 24942738309860, 253566501600240, 2643729700672284, 28259635983501165, 309569087038701420
(list; graph; refs; listen; history; internal format)
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OFFSET
| 8,1
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COMMENTS
| Number of partitions enumerated by A105481 in which the maximal length of consecutive integers in a block is 2.
With offset 4t, number of partitions of {1...N} containing 4 detached strings of t consecutive integers, where N=n+4j, 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 four t-strings.
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REFERENCES
| 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
| A. O. Munagi, Set Partitions with Successions and Separations,IJMMS 2005:3 (2005),451-463.
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FORMULA
| a(n)=binomial(n-4, 4)*Bell(n-5), which is the case r=4 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
| a(8) = 5 because the partitions of {1,...,8} with 4 detached pairs of consecutive integers are 1256/3478, 1256/34/78, 12/3478/56, 1278/34/56, 12/34/56/78.
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MAPLE
| seq(binomial(n-4, 4)*combinat[bell](n-5), n=8..28);
a:=n->sum(numbcomb(n, 3)*bell(n)/4, j=0..n): seq(a(n), n=3..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007
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CROSSREFS
| Cf. A105481, A105489, A105491, A105486.
Sequence in context: A151752 A127212 A091903 * A105494 A030986 A091882
Adjacent sequences: A105487 A105488 A105489 * A105491 A105492 A105493
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KEYWORD
| easy,nonn
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AUTHOR
| A. O. Munagi (amunagi(AT)yahoo.com), Apr 10 2005
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