A322759 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).

1, 2, 500, 406594944, 17946021496671970416, 266763232240477060473636852903291418, 1455102310580730414248044171189633697513044431339233543733641216

Offset

0,2

Comments

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

References

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

Links

Table of n, a(n) for n=0..6.

Example

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

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)];

Crossrefs

Cf. A000984, A008793, A322760.

Sequence in context: A087615 A027655 A220859 * A178468 A024032 A172232

Adjacent sequences: A322756 A322757 A322758 * A322760 A322761 A322762

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 28 2018

Status

approved