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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 (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  ((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

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