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A215571 Number of permutations of n indistinguishable copies of 1..6 with every partial sum <= the same partial sum averaged over all permutations.

%I A215571 #10 Sep 07 2016 04:01:23
%S A215571 1,139,746192,9212531290,164401445439455,3611684199828856072,
%T A215571 90695437030756958966384,2500267880518574604245088816,
%U A215571 73839261438738554611424321993670,2299118288652572230673921886739695630,74651909129454094524656449803220566122458
%N A215571 Number of permutations of n indistinguishable copies of 1..6 with every partial sum <= the same partial sum averaged over all permutations.
%H A215571 Vaclav Kotesovec, <a href="/A215571/b215571.txt">Table of n, a(n) for n = 0..26</a>
%e A215571 a(1) = 139: (1,2,3,4,5,6), (1,2,3,4,6,5), ..., (3,4,2,1,6,5), (3,4,2,5,1,6).
%p A215571 b:= proc(l) option remember; local m, n, g;
%p A215571       m, n:= nops(l), add(i, i=l);
%p A215571       g:= add(i*l[i], i=1..m)-(m+1)/2*(n-1);
%p A215571      `if`(n<2, 1, add(`if`(l[i]>0 and i<=g,
%p A215571         b(subsop(i=l[i]-1, l)), 0), i=1..m))
%p A215571     end:
%p A215571 a:= n-> b([n$6]):
%p A215571 seq(a(n), n=0..6);
%Y A215571 Row n=6 of A215561.
%K A215571 nonn
%O A215571 0,2
%A A215571 _Alois P. Heinz_, Aug 16 2012