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Numerator of Product_{i=1..n, j=1..n, k=1..n, m=1..n} (i+j+k+m-2)/(i+j+k+m-3).
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%I #12 Jan 03 2021 23:35:34

%S 1,2,500,406594944,17946021496671970416,

%T 266763232240477060473636852903291418,

%U 1455102310580730414248044171189633697513044431339233543733641216

%N Numerator of Product_{i=1..n, j=1..n, k=1..n, m=1..n} (i+j+k+m-2)/(i+j+k+m-3).

%C The sequence of rationals A322759/A322760 is the natural successor to A000984 and A008793.

%D Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 576, line 3, with a=b=c=d=n.

%e 1, 2, 500/3, 406594944/25, 17946021496671970416/343, 266763232240477060473636852903291418/1701, ...

%p f4:=proc(n) local a,i,j,k,m;

%p a:=1;

%p for i from 1 to n do

%p for j from 1 to n do

%p for k from 1 to n do

%p for m from 1 to n do

%p a:=a*(i+j+k+m-2)/(i+j+k+m-3); od: od: od: od: a; end;

%p t1 := [seq(f4(n),n=0..12)];

%Y Cf. A000984, A008793, A322760.

%K nonn,frac

%O 0,2

%A _N. J. A. Sloane_, Dec 28 2018