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%I #40 Mar 21 2023 15:41:10
%S 8,192,92160,743178240,97029351014400,203286581427673497600,
%T 6819500449352277792129024000,3660967964237442812098963052691456000,
%U 31446995505814020383166371418359014222725120000
%N Order of complex Clifford group of degree 2^n arising in quantum coding theory.
%H T. D. Noe, <a href="/A003956/b003956.txt">Table of n, a(n) for n = 0..20</a>
%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. Nebe, E. M. Rains and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0001038">The invariants of the Clifford groups</a>, arXiv:math/0001038 [math.CO], 2000; Des. Codes Crypt. 24 (2001), 99-121.
%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.
%H Edwin Pednault, <a href="https://arxiv.org/abs/2303.08287">An alternative approach to optimal wire cutting without ancilla qubits</a>, arXiv:2303.08287 [quant-ph], 2023.
%H Tefjol Pllaha, Olav Tirkkonen, and Robert Calderbank, <a href="https://arxiv.org/abs/2102.12384">Binary Subspace Chirps</a>, arXiv:2102.12384 [cs.IT], 2021.
%H B. Runge, <a href="https://doi.org/10.1016/0012-365X(94)00271-J">Codes and Siegel modular forms</a>, Discrete Math. 148 (1996), 175-204.
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%p a(n):= 2^(n^2+2*n+3)*mul(4^j-1, j=1..n); seq(a(n), n=0..10); # modified by _G. C. Greubel_, Sep 24 2019
%t Table[2^(n^2+2n+3) Product[4^j-1,{j,n}],{n,0,10}] (* _Harvey P. Dale_, Nov 03 2017 *)
%o (PARI) vector(11, n, 2^(n^2 +2)*prod(j=1,n-1, 4^j-1) ) \\ _G. C. Greubel_, Sep 24 2019
%o (Magma) [n eq 0 select 8 else 2^((n+1)^2+2)*(&*[4^j-1: j in [1..n]]): n in [0..10]]; // _G. C. Greubel_, Sep 24 2019
%o (Sage) [2^((n+1)^2 +2)*product(4^j -1 for j in (1..n)) for n in (0..10)] # _G. C. Greubel_, Sep 24 2019
%o (GAP) List([0..10], n-> 2^((n+1)^2 +2)*Product([1..n], j-> 4^j -1) ); # _G. C. Greubel_, Sep 24 2019
%o (Python)
%o from math import prod
%o def A003956(n): return prod((1<<i)-1 for i in range(2,2*n+1,2)) << n*(n+2)+3 # _Chai Wah Wu_, Jun 20 2022
%Y Cf. A001309, A014116, A014115, A027672.
%Y Equals twice A027638.
%K nonn,easy,nice
%O 0,1
%A _N. J. A. Sloane_, _Peter Shor_
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