login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A192553 Sums of powers of permutations of length n. 0
1, 2, 5, 15, 51, 197, 850, 3897, 19461, 104264 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Permutations of length n can be represented by an ordered list of the first n integers. Summing vertically the lists corresponding to the successive powers of a permutation up to its order ord, gives a new list of n integers from ord to n*ord. a(n) gives the number of different such lists. a(n) is related to the Bell numbers and majored by them, as permutations with the same cycle decomposition will have the same order and only a different ordering of powers.
LINKS
FORMULA
a(n) <= Bell(n)
EXAMPLE
{2, 1, 3, 6, 4, 5} is a permutation of length 6 and order 6. Its successive powers are
{2, 1, 3, 6, 4, 5},
{1, 2, 3, 5, 6, 4},
{2, 1, 3, 4, 5, 6},
{1, 2, 3, 6, 4, 5},
{2, 1, 3, 5, 6, 4},
{1, 2, 3, 4, 5, 6}. Their sum is
{9, 9, 18, 30, 30, 30} or
{8, 7, 15, 26, 25, 24} if one does not includes the identity.
There are 197 different sums for n=6.
CROSSREFS
Sequence in context: A201168 A001681 A343665 * A053553 A276721 A287583
KEYWORD
nonn
AUTHOR
Olivier Gérard, Jul 04 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)