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 A227404 Total number of inversions in all permutations of order n consisting of a single cycle. 3
 0, 0, 1, 4, 22, 140, 1020, 8400, 77280, 786240, 8769600, 106444800, 1397088000, 19718899200, 297859161600, 4794806016000, 81947593728000, 1482030950400000, 28277150533632000, 567677135241216000, 11961768206868480000, 263969867887165440000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The formula trivially follows from the observation that every pair of elements i2, a(n) = n! * (3*n-1)/12. - Vaclav Kotesovec, Feb 14 2014 EXAMPLE a(3) = 4 because the cyclic 3-permutations: (1,2,3), (1,3,2) written in one line (sequence) notation: {2,3,1}, {3,1,2} have 2 + 2 = 4 inversions. MATHEMATICA Table[Total[Map[Inversions, Map[FromCycles, Map[List, Map[Prepend[#, n]&, Permutations[n-1]]]]]], {n, 1, 8}] CROSSREFS Cf. A001809, A211606, A216239. Sequence in context: A181784 A003287 A077056 * A366677 A190271 A045744 Adjacent sequences: A227401 A227402 A227403 * A227405 A227406 A227407 KEYWORD nonn AUTHOR Geoffrey Critzer, Sep 21 2013 EXTENSIONS a(13)-a(15) from Alois P. Heinz, Sep 26 2013 Terms a(16) and beyond from Max Alekseyev, Jan 05 2018 STATUS approved

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Last modified December 4 11:57 EST 2023. Contains 367560 sequences. (Running on oeis4.)