A124996 a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1/x^k)^4.

1, 6, 44, 426, 4658, 55260, 689508, 8914872, 118374410, 1604658420, 22115171280, 308940507202, 4364729023812, 62256518307724, 895294865045296, 12966655239260890, 188967013096930258, 2769003814616561636, 40773380119956434784, 603008173331642200144

Offset: 0

Author

N. J. A. Sloane, Jul 12 2008

Keywords

• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 0..834 (terms < 10^1000)

Crossrefs

For constant term in expansion of Product_{k=1..n} (x^k + 1/x^k)^q for other values of q see A063865, A047653, A124995.

Programs

PARI

a(n) = polcoef(prod(k=1, n, (x^k + 1/x^k)^4), 0); \\ Michel Marcus, Jan 07 2021

Formula

a(n) ~ sqrt(3) * 16^n / (sqrt(2*Pi) * n^(3/2)). - Vaclav Kotesovec, Jan 07 2021