A285382 Sum of entries in the last cycles of all permutations of [n].

1, 5, 25, 143, 942, 7074, 59832, 563688, 5858640, 66622320, 823055040, 10979133120, 157300375680, 2409321801600, 39290164300800, 679701862425600, 12433400027596800, 239791474805299200, 4863054420016128000, 103462238924835840000, 2304147629440419840000

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 A366221 A371725

Adjacent sequences: A285379 A285380 A285381 * A285383 A285384 A285385

Keyword

nonn

Author

Alois P. Heinz, Apr 20 2017

Status

approved