A092301 a(n) = 3^(n^2+2n+1)*Product_{j=1..n} (9^j-1).

3, 648, 12597120, 20056328248320, 2589682730460637593600, 27088537289801063207068178841600, 22951765904242357263319251737033603284992000, 1575188025865853631043462731239785102397842258177032192000, 8756565436081269687990149660909266003169595871730647160978999995269120000

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, A132037.

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[3^(n^2+2n+1) Product[9^j-1,{j,n}],{n,0,10}] (* Harvey P. Dale, Jun 23 2013 *)

Formula

From Amiram Eldar, Jul 07 2025: (Start)

a(n) = A092299(n) / 4.

a(n) ~ c * 3^(2*n^2+3*n+1), where c = A132037. (End)