|
| |
|
|
A089039
|
|
Number of circular permutations of 2n letters that are free of jealousy.
|
|
0
|
|
|
|
1, 2, 6, 60, 960, 24000, 861840, 42104160, 2686763520, 217039253760, 21651071904000, 2614084251609600, 375698806311628800, 63383303286471168000, 12403896267489382656000, 2786994829444848422400000, 712575504763406361133056000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The number of circular permutations of 2*n people consisting of n married couples, such that no one sits next to a person of the opposite sex who is not his or her spouse.
When n -> infinity, a(n)/(n-1)!^2 -> Sum 1/(k!*(k-1)!), k=1,2,... = 1.590636854637329063382254424999666247954478159495536647132...
|
|
|
LINKS
|
Table of n, a(n) for n=1..17.
Masaru Yoshikawa, Arithmetic challenges. See problem No. 380.
Eiji Kurihara, Small room of mathematics; see the answer for No. 380 of arithmetic challenges version 1.
|
|
|
FORMULA
|
a(1)=1, a(n)=Sum (n!*(n-k-1)!^2)/((k-1)!^2*(n-2*k)!*k), k=1...[n/2], if n>1
|
|
|
EXAMPLE
|
a(3)=6 because ABCcba,ACBbca,ABbacC,ACcabB,AabcCB,AacbBC are possible.
|
|
|
CROSSREFS
|
Sequence in context: A156972 A086332 A180402 * A156451 A152617 A156472
Adjacent sequences: A089036 A089037 A089038 * A089040 A089041 A089042
|
|
|
KEYWORD
|
nonn,nice
|
|
|
AUTHOR
|
Akemi Nakamura, Michihiro Takahashi, Shogaku Meitantei, (naka(AT)sansu.org), Dec 03 2003
|
|
|
STATUS
|
approved
|
| |
|
|
