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 A105482 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. 5
 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; text; internal format)
 OFFSET 6,2 REFERENCES A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451-463. LINKS A. O. Munagi, Set Partitions with Successions and Separations,IJMMS 2005:3 (2005),451-463. 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 Janjic, Jul 08 2010] 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. MAPLE seq(binomial(n-1, 5)*combinat[bell](n-6), n=6..26); CROSSREFS Cf. A105481, A105487, A105491. Sequence in context: A074429 A062310 A229247 * A242158 A157335 A057089 Adjacent sequences:  A105479 A105480 A105481 * A105483 A105484 A105485 KEYWORD easy,nonn AUTHOR Augustine O. Munagi, Apr 10 2005 STATUS approved

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Last modified November 12 04:21 EST 2019. Contains 329051 sequences. (Running on oeis4.)