A147682 Late-growing permutations: number of permutations of 2 indistinguishable copies of 1..n with every partial sum <= the same partial sum averaged over all permutations.

1, 1, 2, 30, 403, 18720, 746192, 71892912, 5873837638, 951265850580, 133244998049858, 32484245570649180, 6956417433946216990, 2375465385671586163800, 723157816455776560763294, 329255781245519867317200240, 135189844328107458501296074066, 79079768375837127458516103725820

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Maple

b:= proc(l) option remember; local m, n, g;
      m, n:= nops(l), add(i, i=l);
      g:= add(i*l[i], i=1..m)-(m+1)/2*(n-1);
     `if`(n<2, 1, add(`if`(l[i]>0 and i<=g,
        b(subsop(i=l[i]-1, l)), 0), i=1..m))
    end:
a:= n-> b([2$n]):
seq(a(n), n=1..10);  # Alois P. Heinz, Aug 16 2012

Mathematica

b[l_List] := b[l] = Module[{m, n, g}, {m, n} = {Length[l], Total[l]}; g = Sum[i* l[[i]], {i, 1, m}] - (m+1)/2*(n-1); If[n<2, 1, Sum[If[l[[i]]>0 && i <= g, b[ ReplacePart[l, i -> l[[i]]-1]], 0], {i, 1, m}]]]; a[n_] := b[Table[2, {n}]]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Mar 13 2015, after Alois P. Heinz *)

Crossrefs

Cf. A147681.

Column k=2 of A215561.

Sequence in context: A083446 A230726 A091345 * A211906 A077517 A060042

Adjacent sequences: A147679 A147680 A147681 * A147683 A147684 A147685

Keyword

nonn,hard

Author

R. H. Hardin, May 01 2009

Extensions

a(14) from Alois P. Heinz, Aug 16 2012

a(15) from Alois P. Heinz, Nov 02 2014

a(16) from Vaclav Kotesovec, Sep 07 2016

a(17) from Vaclav Kotesovec, Sep 08 2016

Status

approved