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A213344 2-quantum transitions in systems of N>=2 spin 1/2 particles, in columns by combination indices.

%I A213344 #30 Nov 18 2019 22:06:47
%S A213344 1,6,24,4,80,40,240,240,15,672,1120,210,1792,4480,1680,56,4608,16128,
%T A213344 10080,1008,11520,53760,50400,10080,210,28160,168960,221760,73920,
%U A213344 4620,67584,506880,887040,443520,55440,792
%N A213344 2-quantum transitions in systems of N>=2 spin 1/2 particles, in columns by combination indices.
%C A213344 For a general discussion, please see A213343.
%C A213344 This a(n) is for double-quantum transitions (q = 2).
%C A213344 It lists the flattened triangle T(2;N,k) with rows N = 2,3,... and columns N, k = 0..floor((N-2)/2).
%D A213344 See A213343.
%H A213344 Stanislav Sykora, <a href="/A213344/b213344.txt">Table of n, a(n) for n = 2..2501</a>
%H A213344 Stanislav Sykora, <a href="/A213344/a213344.txt">T(2;N,k) with rows N=2,..,100 and columns k=0,..,floor((N-2)/2)</a>
%H A213344 Stanislav Sýkora, <a href="http://www.ebyte.it/stan/blog12to14.html#14Dec31">Magnetic Resonance on OEIS</a>, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
%F A213344 Set q = 2 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).
%e A213344 For N=4, there are 4 second-quantum transitions with combination index 1: (0001,1110),(0010,1101),(0100,1011),(1000,0111).
%e A213344 Starting rows of the triangle:
%e A213344   N | k = 0, 1, ..., floor((N-2)/2)
%e A213344   2 |   1
%e A213344   3 |   6
%e A213344   4 |  24   4
%e A213344   5 |  80  40
%e A213344   6 | 240 240 15
%t A213344 With[{q = 2}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 12}, {k, 0, Floor[(n - 2)/2]}]] // Flatten (* _Michael De Vlieger_, Nov 18 2019 *)
%o A213344 (PARI) See A213343; set thisq = 2.
%Y A213344 Cf. A051288 (q=0), A213343 (q=1), A213345 to A213352 (q=3..10).
%Y A213344 Cf. A001788 (first column), A002694 (row sums).
%K A213344 nonn,tabf
%O A213344 2,2
%A A213344 _Stanislav Sykora_, Jun 09 2012