%I #7 Jan 03 2021 23:23:16
%S 1,3,25,343,1701,117406179,1377144939510210299,7319582701014978251,
%T 68957488738377254912,31655878065328599351648522128233122128960851,
%U 509835253962108047546712884688217781173085736103608399459708858847501357,254487582354743232569912323057838854214490688232159609663484703619
%N Denominator 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, A322759.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Dec 28 2018