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 A225617 Number of (strict) inversions in all standard Young tableaux of size n. 2
 0, 0, 1, 7, 39, 188, 884, 4116, 19108, 89926, 427386, 2068934, 10163358, 50888024, 258983668, 1342912608, 7079970072, 38000183102, 207309599246, 1150329076074, 6484351459090, 37143321514076, 216001121263896, 1275332898098744, 7639400455469944, 46423461664822648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A (strict) inversion is a pair of cells (i,j) with i`if`(j=1, 0, l[j-1]), (f->f+[0, f[1]*       add(l[h]-l[j], h=j+1..nops(l))])       (b(subsop(j=l[j]-1, l))), 0), j=1..nops(l)))     end: g:= proc(n, i, l) `if`(n=0 or i=1, b([1\$n, l[]]),       `if`(i<1, 0, g(n, i-1, l)+       `if`(i>n, 0, g(n-i, i, [i, l[]]))))     end: a:= n-> g(n\$2, [])[2]: seq(a(n), n=1..23);  # Alois P. Heinz, Aug 09 2013 MATHEMATICA inversions[t_?TableauQ]:= Block[{t0}, t0=(First[Position[t, #1]]&) /@ Range[Max[t]]; Cases[Table[{i, j}, {j, 2, Max[t]}, {i, j-1}], {i_, j_}/; MatchQ[t0[[i]]-t0[[j]], {_?Negative, _?Positive}]->{i, j}, {2}]]; Table[Tr[Length[inversions[#]]& /@ Tableaux[n]], {n, 13}] CROSSREFS Cf. A225618 (weak inversions), A161125 (descent numbers). Cf. A000085 (Young tableaux with n cells). Sequence in context: A027482 A196782 A128554 * A032207 A004057 A081898 Adjacent sequences:  A225614 A225615 A225616 * A225618 A225619 A225620 KEYWORD nonn AUTHOR Wouter Meeussen, Aug 04 2013 EXTENSIONS Terms verified and more terms added, Joerg Arndt, Aug 07 2013 a(19)-a(26) from Alois P. Heinz, Aug 08 2013 STATUS approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)