A134373 -id:A134373 - cp's OEIS frontend

A134375 a(n) = (n!)^4.

1, 1, 16, 1296, 331776, 207360000, 268738560000, 645241282560000, 2642908293365760000, 17340121312772751360000, 173401213127727513600000000, 2538767161403058526617600000000, 52643875858853821607942553600000000, 1503561738404723998944447273369600000000

Offset: 0

Artur Jasinski, Oct 22 2007

nonn

a(n) is also the determinant of the symmetric n X n matrix M defined by M(i,j) = sigma_4(gcd(i,j)) for 1 <= i,j <= n, and n>0, where sigma_4 is A001159. - Enrique Pérez Herrero, Aug 13 2011

Alois P. Heinz, Table of n, a(n) for n = 0..100

Cf. A000142, A001044, A000442, A036740, A010050, A009445, A134366, A134367, A134368, A134369, A134371, A134372, A134373, A134374.

Row n=4 of A225816.

a:= n-> (n!)^4:
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 15 2013

Mathematica
```
Table[((n)!)^(4), {n, 0, 10}]
```

a(n) = det(S(i+4,j), 1 <= i,j <= n), where S(n,k) are Stirling numbers of the second kind. - Mircea Merca, Apr 04 2013

A134374 a(n) = ((2n+1)!)^2.

Original entry on oeis.org

1, 36, 14400, 25401600, 131681894400, 1593350922240000, 38775788043632640000, 1710012252724199424000000, 126513546505547170185216000000, 14797530453474819213543604224000000

Offset: 0

Artur Jasinski, Oct 22 2007

Cf. A000142, A001044, A000442, A036740, A010050, A009445, A134366, A134367, A134368, A134369, A134371, A134372, A134373, A134375, A334378.

A134374:=n->((2*n+1)!)^2; seq(A134374(n), n=0..10); # Wesley Ivan Hurt, May 02 2014

Mathematica
```
Table[((2n+1)!)^(2), {n, 0, 10}]
```

a(n) = ((2*n+1)!)^2; \\ Michel Marcus, Nov 16 2020

a(n) = A009445(n)^2 = A001044(2n+1). - Wesley Ivan Hurt, May 02 2014
From Amiram Eldar, Nov 16 2020: (Start)
Sum_{n>=0} 1/a(n) = A334378.
Sum_{n>=0} (-1)^n/a(n) = Im(BesselJ(0, 2*exp(3*Pi*i/4))). (End)

A127488 a(n) = (n^2)!/(2*(n!)).

Original entry on oeis.org

6, 30240, 435891456000, 64630041847212441600000, 258328699159653623241666283438080000000

Offset: 2

Artur Jasinski, Jan 16 2007

nonn

Cf. A000142, A001044, A000442, A036740, A010050, A009445, A134366, A134367, A134368, A134369, A134371, A134372, A134373, A134374, A134374

Mathematica
```
Table[(n^2)!/(2(n!)), {n, 2, 6}]
```

a(n) ~ n^(2*n^2 - n + 1/2) / (2 * exp(n*(n-1))). - Vaclav Kotesovec, Oct 26 2017

cp's OEIS Frontend

A134375 a(n) = (n!)^4.

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A134374 a(n) = ((2n+1)!)^2.

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A127488 a(n) = (n^2)!/(2*(n!)).

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