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A322760 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).

%I A322760 #11 Mar 16 2025 09:27:14
%S A322760 1,1,3,25,343,1701,117406179,1377144939510210299,7319582701014978251,
%T A322760 68957488738377254912,31655878065328599351648522128233122128960851,
%U A322760 509835253962108047546712884688217781173085736103608399459708858847501357,254487582354743232569912323057838854214490688232159609663484703619
%N A322760 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 A322760 The sequence of rationals A322759/A322760 is the natural successor to A000984 and A008793.
%D A322760 Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 576, line 3, with a=b=c=d=n.
%e A322760 1, 2, 500/3, 406594944/25, 17946021496671970416/343, 266763232240477060473636852903291418/1701, ...
%p A322760 f4:=proc(n) local a,i,j,k,m;
%p A322760 a:=1;
%p A322760 for i from 1 to n do
%p A322760 for j from 1 to n do
%p A322760 for k from 1 to n do
%p A322760 for m from 1 to n do
%p A322760 a:=a*(i+j+k+m-2)/(i+j+k+m-3); od: od: od: od: a; end;
%p A322760 t1 := [seq(f4(n),n=0..12)];
%o A322760 (PARI) a(n) = denominator(prod(i=1,n,prod(j=1,n,prod(k=1,n,prod(m=1,n,(i+j+k+m-2)/(i+j+k+m-3)))))) \\ _Georg Fischer_, Mar 16 2025
%Y A322760 Cf. A000984, A008793, A322759.
%K A322760 nonn,frac
%O A322760 0,3
%A A322760 _N. J. A. Sloane_, Dec 28 2018
%E A322760 1 prepended by _Georg Fischer_, Mar 16 2025