|
| |
|
|
A006198
|
|
Number of partitions into pairs.
(Formerly M4241)
|
|
1
| |
|
|
1, 1, 6, 41, 365, 3984, 51499, 769159, 13031514, 246925295, 5173842311, 118776068256, 2964697094281, 79937923931761, 2315462770608870, 71705109685449689
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| a(n) is the subset of the set of unordered pairings of the first 2n integers (A001147) forbidding pairs of the form (i,i+1) for all i in [2,n-1]. There are many other selections of forbidden pairs giving the same count. [From Olivier Gérard, Feb 8 2011]
|
|
|
REFERENCES
| G. Kreweras and Y. Poupard, Sur les partitions en paires d'un ensemble fini totalement ordonne, Publications de l'Institut de Statistique de l'Universit\'{e} de Paris, 23 (1978), 57-74.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
FORMULA
| a(n) = |A000806(n-1)|+|A000806(n)|. G.f.: Sum_{n>=0} A001147(n)*(x/(1+x)^2)^n. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 27 2007
|
|
|
CROSSREFS
| Sequence in context: A184140 A094869 A178824 * A167588 A007130 A075000
Adjacent sequences: A006195 A006196 A006197 * A006199 A006200 A006201
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
