|
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 4,2
|
|
|
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, Int. J. Math. Math. Sci. (IJMMS) vol 2005 no 3 (2005) pp 451-463.
|
|
|
FORMULA
| a(n) = binomial(n-1, 3)Bell(n-4), the case r = 3 in the general case of r pairs: c(n, r) = binomial(n-1, r)B(n-r-1).
O.g.f. for c(n,r) is exp(-1)*Sum(x^(r+1)/(n!*(1-n*x)^(r+1)),n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2008
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>=3, a(n+1)=(-1)^(n-3)coeff(charpoly(A,x),x^3). [From Milan R. Janjic (agnus(AT)blic.net), 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(n-1, 3)*combinat[bell](n-4), n=4..25);
|
|
|
CROSSREFS
| Cf. A105479, A105481, A105485, A105490.
Sequence in context: A178874 A103771 A005054 * A186369 A093440 A168606
Adjacent sequences: A105477 A105478 A105479 * A105481 A105482 A105483
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| A. O. Munagi (amunagi(AT)yahoo.com), Apr 10 2005
|
| |
|
|
