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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 than 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; refs; listen; history; internal format)
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OFFSET
| 5,2
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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, 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).
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>=4, a(n+1)=(-1)^(n-4)coeff(charpoly(A,x),x^4). [From Milan R. Janjic (agnus(AT)blic.net), Jul 08 2010]
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EXAMPLE
| 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
| seq(binomial(n-1, 4)*combinat[bell](n-5), n=5..25);
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CROSSREFS
| Cf. A105480, A105482, A105486, A105491, A105494.
Sequence in context: A111469 A057088 A156195 * A094167 A051738 A052934
Adjacent sequences: A105478 A105479 A105480 * A105482 A105483 A105484
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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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