A090768 a(n) = 4*7^(n^2+2n+1)*Product_{j=1..n} (49^j-1).

28, 460992, 18594942105600, 1801630225452634420838400, 419114092659655895262507217606410240000, 234094442205343557204838431982679810784254737891983360000, 313936710456644712932526713436974934772339799367593873556694922893983744000000, 1010846620958915523772074873493863525346718205399610275113597795065777917926818948851860049494016000000

Offset: 0

Author

N. J. A. Sloane, Feb 10 2004

Keywords

• nonn

Comments

The order of the p-Clifford group for an odd prime p is a*p^(n^2+2n+1)*Product_{j=1..n} (p^(2*j)-1), where a = gcd(p+1,4).

Links

• G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Crossrefs

Cf. A001309, A003956.

Cf. A092299 and A092301 (p=3), A092300 and A089989 (p=5), A090768 and A090769 (p=7), A090770 (p=2, although this is the wrong formula in that case).

Programs

Mathematica

a[n_] := 4*7^(n^2+2*n+1) * Product[49^j - 1, {j, 1, n}]; Array[a, 10, 0] (* Amiram Eldar, Jul 07 2025 *)

Formula

From Amiram Eldar, Jul 07 2025: (Start)

a(n) = 4 * A090769(n).

a(n) ~ c * 7^(2*n^2+3*n+1), where c = 4 * Product_{k>=1} (1 - 1/7^(2*k)) = 3.916701388593... . (End)