|
Search: id:A140456
|
|
|
| A140456 |
|
a(n) = the number of indecomposable involutions of length n. |
|
+0
2
|
|
| 1, 1, 1, 3, 7, 23, 71, 255, 911, 3535, 13903, 57663, 243871, 1072031, 4812575, 22278399, 105300287, 510764095, 2527547455, 12794891007, 66012404863, 347599231103, 1863520447103, 10178746224639, 56548686860543
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
An involution is a self-inverse permutation. A permutation of [n] = {1, 2, ..., n} is indecomposable if it does not fix [j] for any 0 < j < n.
|
|
LINKS
|
Joel Brewster Lewis (jblewis(AT)post.harvard.edu), Jul 22 2008, Table of n, a(n) for n = 1..50
|
|
FORMULA
|
Generating function is 1 - 1/I(x), where I(x) is the ordinary generating function for involutions (A000085).
|
|
EXAMPLE
|
The unique indecomposable involution of length 3 is 321. The indecomposable involutions of length 4 are 3412, 4231 and 4321.
|
|
MATHEMATICA
|
CoefficientList[Series[1 - 1/Total[CoefficientList[Series[E^(x + x^2/2), {x, 0, 50}], x] * Range[0, 50]! * x^Range[0, 50]], {x, 0, 50}], x]
|
|
CROSSREFS
|
Cf. cf. A000085 (involutions) and A003319 (indecomposable permutations).
Sequence in context: A148703 A045610 A045723 this_sequence A066768 A062241 A000229
Adjacent sequences: A140453 A140454 A140455 this_sequence A140457 A140458 A140459
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Joel Brewster Lewis (jblewis(AT)post.harvard.edu), Jul 22 2008
|
|
|
Search completed in 0.002 seconds
|
