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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.

%I A147682 #22 Sep 08 2016 09:40:28
%S A147682 1,1,2,30,403,18720,746192,71892912,5873837638,951265850580,
%T A147682 133244998049858,32484245570649180,6956417433946216990,
%U A147682 2375465385671586163800,723157816455776560763294,329255781245519867317200240,135189844328107458501296074066,79079768375837127458516103725820
%N 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.
%p A147682 b:= proc(l) option remember; local m, n, g;
%p A147682       m, n:= nops(l), add(i, i=l);
%p A147682       g:= add(i*l[i], i=1..m)-(m+1)/2*(n-1);
%p A147682      `if`(n<2, 1, add(`if`(l[i]>0 and i<=g,
%p A147682         b(subsop(i=l[i]-1, l)), 0), i=1..m))
%p A147682     end:
%p A147682 a:= n-> b([2$n]):
%p A147682 seq(a(n), n=1..10);  # _Alois P. Heinz_, Aug 16 2012
%t A147682 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_ *)
%Y A147682 Cf. A147681.
%Y A147682 Column k=2 of A215561.
%K A147682 nonn,hard
%O A147682 0,3
%A A147682 _R. H. Hardin_, May 01 2009
%E A147682 a(14) from _Alois P. Heinz_, Aug 16 2012
%E A147682 a(15) from _Alois P. Heinz_, Nov 02 2014
%E A147682 a(16) from _Vaclav Kotesovec_, Sep 07 2016
%E A147682 a(17) from _Vaclav Kotesovec_, Sep 08 2016