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

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

Offset: 0

Author

Artur Jasinski, Oct 22 2007

Keywords

• nonn

Comments

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

Links

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

Crossrefs

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

Row n=4 of A225816.

Programs

Maple

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

Mathematica

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

Formula

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