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%I #15 Jun 20 2022 19:15:31
%S 2,48,23040,185794560,24257337753600,50821645356918374400,
%T 1704875112338069448032256000,915241991059360703024740763172864000,
%U 7861748876453505095791592854589753555681280000,1080506416218846625176535970968094253434513802154475520000,2376056471052200653607636735377527394627947719754523173734842368000000
%N a(n) = 2^(n^2 + 2n + 1)*Product_{j=1..n} (4^j - 1).
%C 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). This is the sequence obtained by (illegally) setting p = 2.
%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.
%t Table[2^(n^2+2n+1) Product[4^j-1,{j,n}],{n,0,10}] (* _Harvey P. Dale_, May 14 2022 *)
%o (Python)
%o from math import prod
%o def A090770(n): return prod((1<<i)-1 for i in range(2,2*n+1,2)) << (n+1)**2 # _Chai Wah Wu_, Jun 20 2022
%Y Cf. A001309, A003956.
%Y Cf. A092299 and A092301 (p=3), A092300 and A089989 (p=5), A090768 and A090769 (p=7).
%Y A bisection of A003053, cf. A003923.
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Feb 10 2004
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