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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
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
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
Column k=1 of A286231.
Sequence in context: A122441 A114870 A222676 * A199319 A366221 A371725
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 20 2017
STATUS
approved