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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.
2
1, 1, 2, 30, 403, 18720, 746192, 71892912, 5873837638, 951265850580, 133244998049858, 32484245570649180, 6956417433946216990, 2375465385671586163800, 723157816455776560763294, 329255781245519867317200240, 135189844328107458501296074066, 79079768375837127458516103725820
OFFSET
0,3
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
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