|
Search: id:A105479
|
|
| |
|
| 0, 0, 1, 3, 12, 50, 225, 1092, 5684, 31572, 186300, 1163085, 7654350, 52928460, 383437327, 2902665885, 22907918640, 188082362120, 1603461748491, 14169892736484, 129594593170210, 1224875863061970, 11948280552370932
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Number of blocks of size 2 in all set partitions of {1,2,...,n}. Example: a(3)=3 because the set partitions of {1,2,3} are 1|2|3, 1|23, 12|3, 13|2, and 123, containing exactly 3 blocks of size 2. a(n)=Sum(k*A124498(n-1,k), k>=0}. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 06 2006
Number of partitions of {1...n} containing 2 pairs of consecutive integers, where each pair is counted within a block and a string of more that 2 consecutive integers are counted two at a time. E.g. a(4) = 3 because the partitions of {1,2,3,4} with 2 pairs of consecutive integers are 123/4,12/34,1/234. - A. O. Munagi (amunagi(AT)yahoo.com), Apr 10 2005
|
|
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, 2)*Bell(n-3), the case r = 2 of the general case of r pairs: c(n, r) = binomial(n-1, r)B(n-r-1).
E.g.f.: z^2/2 * e^(e^z-1) - Frank Ruskey (ruskey(AT)cs.uvic.ca), Dec 26 2006
G.f.: exp(-1)*Sum(x^2/(n!*(1-n*x)^3),n=0..infinity). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 05 2008
|
|
MAPLE
|
[seq(binomial(n, 2)*combinat[bell](n-2), n=0..50)];
|
|
CROSSREFS
|
Cf. A105480, A105489, A105484, A124498.
Sequence in context: A113441 A119976 A074547 this_sequence A094601 A009024 A043291
Adjacent sequences: A105476 A105477 A105478 this_sequence A105480 A105481 A105482
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
A. O. Munagi (amunagi(AT)yahoo.com), Apr 10 2005
|
|
EXTENSIONS
|
Edited by njas, Jan 01 2007
|
|
|
Search completed in 0.002 seconds
|
