A089989 a(n) = 5^(n^2+2n+1)*Product_{j=1..n} (25^j-1).

5, 15000, 29250000000, 35703281250000000000, 27239372138671875000000000000000, 12988743471794208526611328125000000000000000000, 3870947187719439049405530095100402832031250000000000000000000000, 721020100095350865678782984846420731628313660621643066406250000000000000000000000000

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_] := 5^(n^2+2*n+1) * Product[25^j - 1, {j, 1, n}]; Array[a, 10, 0] (* Amiram Eldar, Jul 07 2025 *)

Formula

From Amiram Eldar, Jul 07 2025: (Start)

a(n) = A092300(n) / 2.

a(n) ~ c * 5^(2*n^2+3*n+1), where c = Product_{k>=1} (1 - 1/5^(2*k)) = 0.958400102563... . (End)