login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A285382 Sum of entries in the last cycles of all permutations of [n]. 5
1, 5, 25, 143, 942, 7074, 59832, 563688, 5858640, 66622320, 823055040, 10979133120, 157300375680, 2409321801600, 39290164300800, 679701862425600, 12433400027596800, 239791474805299200, 4863054420016128000, 103462238924835840000, 2304147629440419840000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..449

Wikipedia, Permutation

FORMULA

Recursion: see Maple program.

EXAMPLE

a(3) = 25 because the sum of the entries in the last cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 6+6+3+2+5+3 = 25.

MAPLE

a:= proc(n) option remember; `if`(n<3, n*(3*n-1)/2,

     ((2*n^2+3*n-1)*a(n-1)-(n+2)*(n-1)*n*a(n-2))/(n+1))

    end:

seq(a(n), n=1..25);

MATHEMATICA

Table[n! * (n-1 + 2*(n+1)*HarmonicNumber[n])/4, {n, 1, 25}] (* Vaclav Kotesovec, Apr 29 2017 *)

CROSSREFS

Cf. A284816, A285424, A285439.

Column k=1 of A286231.

Sequence in context: A122441 A114870 A222676 * A199319 A049427 A121639

Adjacent sequences:  A285379 A285380 A285381 * A285383 A285384 A285385

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 20 2017

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 15 18:11 EDT 2021. Contains 345049 sequences. (Running on oeis4.)