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How can i compute the Mahonian number xat row n, index i, without compute previous rows?

Example n := 6, i := 2

row := "1 3 5 6 5 3 1"

x := row[i] //5

Exists therefore an algorithmn / formula?

TTho Einthausend
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    Perhaps see https://math.stackexchange.com/a/1197226 – stark Feb 15 '21 at 23:03
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    @stark: that answer on [math.se] provides the recursion based on the previous row, which I suppose OP already knows since the question is to compute a row *without* first computing the previous rows. – rici Feb 16 '21 at 04:49
  • I haven't looked, but you might try looking at OEIS for this sequence -- in many cases there are some brief notes about algorithms, and at least there are references for further info. – Robert Dodier Feb 16 '21 at 07:29
  • @Robert: It's [OEIS 008302](https://oeis.org/A008302), as indicated in the [math.se] link; the recursion formula presented in that answer is also in OEIS (added by the same person, as it happens). I don't think there's a known closed form, unless it has been very recently discovered. If there is one, it isn't in OEIS either. – rici Feb 16 '21 at 15:40

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