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%I #10 Nov 01 2014 23:02:37
%S 1,1001,71892912,13126885205000,3627155158988429250,
%T 1267664556730792079292048,515544601327354412382720479328,
%U 233099041543988273824859604028713600,113972303622279852972722869873689584148750,59182016901859077504525075283397206729638923750
%N Number of permutations of n indistinguishable copies of 1..7 with every partial sum <= the same partial sum averaged over all permutations.
%H Alois P. Heinz, <a href="/A215593/b215593.txt">Table of n, a(n) for n = 0..11</a>
%e a(1) = 1001: (1,2,3,4,5,6,7), (1,2,3,4,5,7,6), ..., (4,3,5,2,1,7,6), (4,3,5,2,6,1,7).
%p b:= proc(x, y, z, u, v, w, h) option remember; local n, g;
%p n:= x+y+z+u+v+w+h; g:= x+2*y+3*z+4*u+5*v+6*w+7*h -8*(n-1)/2;
%p `if`(n<2, 1, `if`(x>0 and 1<=g, b(x-1, y, z, u, v, w, h), 0)+
%p `if`(y>0 and 2<=g, b(x, y-1, z, u, v, w, h), 0)+
%p `if`(z>0 and 3<=g, b(x, y, z-1, u, v, w, h), 0)+
%p `if`(u>0 and 4<=g, b(x, y, z, u-1, v, w, h), 0)+
%p `if`(v>0 and 5<=g, b(x, y, z, u, v-1, w, h), 0)+
%p `if`(w>0 and 6<=g, b(x, y, z, u, v, w-1, h), 0)+
%p `if`(h>0 and 7<=g, b(x, y, z, u, v, w, h-1), 0))
%p end:
%p a:= n-> b(n$7):
%p seq(a(n), n=0..4);
%Y Row n=7 of A215561.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Aug 16 2012
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