

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
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OFFSET

6,2


REFERENCES

A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451463.


LINKS

Table of n, a(n) for n=6..25.
A. O. Munagi, Set Partitions with Successions and Separations,IJMMS 2005:3 (2005),451463.


FORMULA

a(n) = binomial(n1, 5)Bell(n6), the case r = 5 in the general case of r pairs: c(n, r) = binomial(n1, r)B(nr1).
Let A be the upper Hessenberg matrix of order n defined by: A[i,i1]=1, A[i,j]=binomial(j1,i1), (i<=j), and A[i,j]=0 otherwise. Then, for n>=5, a(n+1)=(1)^(n5)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(n1, 5)*combinat[bell](n6), 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



