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%I #16 Jun 21 2022 05:08:39
%S 2,8,1152,2580480,89181388800,48126558103142400,
%T 409825748158189771161600,55428899652335313894424707072000
%N Order of a certain Clifford group in dimension 2^n (the automorphism group of the Barnes-Wall lattice for n != 3).
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 129.
%H A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, <a href="https://arxiv.org/abs/quant-ph/9608006">Quantum error correction via codes over GF(4)</a>, arXiv:quant-ph/9608006, 1996-1997; IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
%H G. E. Wall, <a href="https://doi.org/10.1017/S0027763000023837">On the Clifford collineation, transform and similarity groups. IV. An application to quadratic forms</a>, Nagoya Math. J., 21 (1962), pp. 199-222.
%H <a href="/index/Ba#BW">Index entries for sequences related to Barnes-Wall lattices</a>
%p 2^(n^2+n+1) * (2^n - 1) * product('2^(2*i)-1','i'=1..n-1);
%o (Python)
%o from math import prod
%o def A014115(n): return 2 if n == 0 else ((1<<n)-1)*prod((1<<i)-1 for i in range(2,2*n-1,2)) << n*(n+1)+1 # _Chai Wah Wu_, Jun 20 2022
%Y Agrees with A014116 except at n=3. Cf. A001309, A003956.
%K nonn
%O 0,1
%A _N. J. A. Sloane_