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 A285795 Sum of the second entries in all cycles of all permutations of [n]. 2
 0, 0, 2, 13, 83, 582, 4554, 39672, 382248, 4044240, 46663920, 583554240, 7865622720, 113711230080, 1755484617600, 28828769356800, 501858148377600, 9232213174732800, 178968924600883200, 3646603415927808000, 77916767838981120000, 1742147265551616000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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 = 0..449 Wikipedia, Permutation EXAMPLE a(3) = 13 because the sum of the second entries in all cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 2+3+2+3+3+0 = 13. MAPLE a:= proc(n) option remember; `if`(n<3, n*(n-1),      ((2*n^2+3*n-1)*a(n-1)-(n-1)*n*(n+2)*a(n-2))/(n+1))     end: seq(a(n), n=0..25); MATHEMATICA Flatten[{0, Table[n! * (2*(n+1)*HarmonicNumber[n] - n - 3)/4, {n, 1, 25}]}] (* Vaclav Kotesovec, Apr 29 2017 *) CROSSREFS Column k=2 of A285793. Cf. A001008, A002805. Sequence in context: A317892 A079752 A156018 * A134148 A164035 A074619 Adjacent sequences:  A285792 A285793 A285794 * A285796 A285797 A285798 KEYWORD nonn AUTHOR Alois P. Heinz, Apr 26 2017 STATUS approved

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Last modified June 12 19:57 EDT 2021. Contains 344962 sequences. (Running on oeis4.)