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 A285793 Sum T(n,k) of the k-th entries in all cycles of all permutations of [n]; triangle T(n,k), n>=1, 1<=k<=n, read by rows. 7
 1, 4, 2, 18, 13, 5, 96, 83, 43, 18, 600, 582, 342, 192, 84, 4320, 4554, 2874, 1824, 1068, 480, 35280, 39672, 26232, 17832, 11784, 7080, 3240, 322560, 382248, 261288, 185688, 131256, 88920, 54360, 25200, 3265920, 4044240, 2834640, 2078640, 1534320, 1110960, 765360, 473760, 221760 (list; table; 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 Table of n, a(n) for n=1..45. Wikipedia, Permutation FORMULA T(n,1) = n * n!. T(n,n) = floor((n-1)!*(n+2)/2). EXAMPLE T(3,2) = 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. Triangle T(n,k) begins: : 1; : 4, 2; : 18, 13, 5; : 96, 83, 43, 18; : 600, 582, 342, 192, 84; : 4320, 4554, 2874, 1824, 1068, 480; : 35280, 39672, 26232, 17832, 11784, 7080, 3240; : 322560, 382248, 261288, 185688, 131256, 88920, 54360, 25200; CROSSREFS Columns k=1-2 give: A001563, A285795. Main diagonal and first lower diagonal give: A038720(n-1) (for n>1), A286175. Row sums give A000142 * A000217 = A180119. Cf. A285439, A285595, A286231. Sequence in context: A074676 A257505 A152883 * A117692 A052966 A305135 Adjacent sequences: A285790 A285791 A285792 * A285794 A285795 A285796 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Apr 26 2017 STATUS approved

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Last modified June 10 17:56 EDT 2023. Contains 363206 sequences. (Running on oeis4.)