|
Search: id:A122949
|
|
|
| A122949 |
|
Number of ordered pairs of permutations generating a transitive group. |
|
+0
2
|
|
| 1, 3, 26, 426, 11064, 413640, 20946960, 1377648720, 114078384000, 11611761920640, 1425189271161600, 207609729886944000, 35419018603306060800, 6996657393055480550400, 1584616114318716544665600
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
From Dixon: The sequence is asymptotic to (n!)^2; when divided by n!^2, it has a high-order asymptotic contact with the probability that two randomly chosen permutations generate the symmetric group. Also: a(n)=(n-1)!*A003319(n+1), where A003319 is the number of connected [or indecomposable] permutations. The coefficients in the asymptotic expansion of a(n)/(n!)^2 are A113869 and in absolute value, they constitute A084357 (number of sets of sets of lists).
|
|
LINKS
|
John D. Dixon, Asymptotics of Generating the Symmetric and Alternating Groups, Electronic Journal of Combinatorics, vol 11(2), R56.
|
|
FORMULA
|
Exponential generating function is: log(1+sum(n!*z^n,n=1..infinity))
|
|
EXAMPLE
|
a(2)=3 because there are 2!*2!=4 pairs of permutations, of which only [(1,1),(1,1)] does not generate a transitive group.
|
|
MAPLE
|
series(log(add(n!*z^n, n=0..Order+2)), z=0):seq(coeff(%, z, j)*j!, j=0..Order);
|
|
CROSSREFS
|
Cf. A003319, A084357, A113869.
Sequence in context: A119293 A136046 A143155 this_sequence A049088 A089041 A059511
Adjacent sequences: A122946 A122947 A122948 this_sequence A122950 A122951 A122952
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Philippe.Flajolet(AT)inria.fr (Philippe.Flajolet(AT)inria.fr), Oct 25 2006
|
|
|
Search completed in 0.002 seconds
|
