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A105482
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Number of partitions of {1...n} containing 5 pairs of consecutive integers, where each pair is counted within a block and a string of more than 2 consecutive integers are counted two at a time.
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5
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1, 6, 42, 280, 1890, 13104, 93786, 694584, 5328180, 42336294, 348272925, 2963993760, 26073738236, 236857536216, 2219777316216, 21441389281680, 213260412549303, 2182163481418536, 22951202450444191, 247914874683742728
(list; graph; refs; listen; history; internal format)
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OFFSET
| 6,2
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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-1, 5)Bell(n-6), the case r = 5 in the general case of r pairs: c(n, r) = binomial(n-1, r)B(n-r-1).
Let A be the upper Hessenberg matrix of order n defined by: A[i,i-1]=-1, A[i,j]=binomial(j-1,i-1), (i<=j), and A[i,j]=0 otherwise. Then, for n>=5, a(n+1)=(-1)^(n-5)coeff(charpoly(A,x),x^5). [From Milan R. Janjic (agnus(AT)blic.net), Jul 08 2010]
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EXAMPLE
| a(7) = 6 because the partitions of {1,2,3,4,5,6,7} with 5 pairs of consecutive integers are 123456/7,12345/67,1234/567,123/4567,12/34567,1/234567.
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MAPLE
| seq(binomial(n-1, 5)*combinat[bell](n-6), n=6..26);
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CROSSREFS
| Cf. A105481, A105487, A105491.
Sequence in context: A158797 A074429 A062310 * A157335 A057089 A110711
Adjacent sequences: A105479 A105480 A105481 * A105483 A105484 A105485
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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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