A090769 a(n) = 7^(n^2+2n+1)*Product_{j=1..n} (49^j-1).

7, 115248, 4648735526400, 450407556363158605209600, 104778523164913973815626804401602560000, 58523610551335889301209607995669952696063684472995840000, 78484177614161178233131678359243733693084949841898468389173730723495936000000, 252711655239728880943018718373465881336679551349902568778399448766444479481704737212965012373504000000

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

Table[7^(n^2 + 2 n + 1)*Product[49^j - 1, {j, n}], {n, 0, 7}] (* Wesley Ivan Hurt, Oct 15 2023 *)

Formula

From Amiram Eldar, Jul 07 2025: (Start)

a(n) = A090768(n) / 4.

a(n) ~ c * 7^(2*n^2+3*n+1), where c = Product_{k>=1} (1 - 1/7^(2*k)) = 0.979175347148... . (End)