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).

1, 1, 3, 25, 343, 1701, 117406179, 1377144939510210299, 7319582701014978251, 68957488738377254912, 31655878065328599351648522128233122128960851, 509835253962108047546712884688217781173085736103608399459708858847501357, 254487582354743232569912323057838854214490688232159609663484703619

Offset: 0

Author

N. J. A. Sloane, Dec 28 2018

Keywords

• nonn
• frac

Comments

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

Examples

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

References

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

Crossrefs

Cf. A000984, A008793, A322759.

Programs

Maple

f4:=proc(n) local a,i,j,k,m;
a:=1;
for i from 1 to n do
for j from 1 to n do
for k from 1 to n do
for m from 1 to n do
a:=a*(i+j+k+m-2)/(i+j+k+m-3); od: od: od: od: a; end;
t1 := [seq(f4(n),n=0..12)];

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

Extensions

1 prepended by Georg Fischer, Mar 16 2025