

A105480


Number of partitions of {1...n} containing 3 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.


8



1, 4, 20, 100, 525, 2912, 17052, 105240, 683100, 4652340, 33168850, 246999480, 1917186635, 15480884720, 129811538960, 1128494172720, 10155257740443, 94465951576560, 907162152191470, 8982422995787780, 91603484234843812
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OFFSET

4,2


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=4..24.
A. O. Munagi, Set partitions with successions and separations, Int. J. Math. Math. Sci. (IJMMS) vol 2005 no 3 (2005) pp 451463.


FORMULA

a(n) = binomial(n1, 3)Bell(n4), the case r = 3 in the general case of r pairs: c(n, r) = binomial(n1, r)B(nr1).
O.g.f. for c(n,r) is exp(1)*Sum(x^(r+1)/(n!*(1n*x)^(r+1)),n=0..infinity).  Vladeta Jovovic, Feb 05 2008
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>=3, a(n+1)=(1)^(n3)coeff(charpoly(A,x),x^3). [From Milan Janjic, Jul 08 2010]


EXAMPLE

a(5) = 4 because the partitions of {1,2,3,4,5} with 3 pairs of consecutive integers are 1234/5,123/45,12/345,1/2345.


MAPLE

seq(binomial(n1, 3)*combinat[bell](n4), n=4..25);


CROSSREFS

Cf. A105479, A105481, A105485, A105490.
Sequence in context: A103771 A005054 A216099 * A242156 A186369 A093440
Adjacent sequences: A105477 A105478 A105479 * A105481 A105482 A105483


KEYWORD

easy,nonn


AUTHOR

Augustine O. Munagi, Apr 10 2005


STATUS

approved



