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A215593 Number of permutations of n indistinguishable copies of 1..7 with every partial sum <= the same partial sum averaged over all permutations. 2

%I

%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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Last modified August 14 18:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)