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A213347 5-quantum transitions in systems of N>=5 spin 1/2 particles, in columns by combination indices.

%I A213347 #20 Nov 18 2019 22:07:07
%S A213347 1,12,84,7,448,112,2016,1008,36,8064,6720,720,29568,36960,7920,165,
%T A213347 101376,177408,63360,3960,329472,768768,411840,51480,715,1025024,
%U A213347 3075072,2306304,480480,20020,3075072,11531520,11531520
%N A213347 5-quantum transitions in systems of N>=5 spin 1/2 particles, in columns by combination indices.
%C A213347 For a general discussion, please see A213343.
%C A213347 This a(n) is for quintuple-quantum transitions (q = 5).
%C A213347 It lists the flattened triangle T(5;N,k) with rows N = 5,6,... and columns N, k = 0..floor((N-5)/2).
%D A213347 See A213343
%H A213347 Stanislav Sykora, <a href="/A213347/b213347.txt">Table of n, a(n) for n = 5..2356</a>
%H A213347 Stanislav Sykora, <a href="/A213347/a213347.txt">T(5;N,k) with rows N=5,..,100 and columns k=0,..,floor((N-5)/2)</a>
%H A213347 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 A213347 Set q = 5 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).
%e A213347 Starting rows of the triangle:
%e A213347   N | k = 0, 1, ..., floor((N-5)/2)
%e A213347   5 |    1
%e A213347   6 |   12
%e A213347   7 |   84    7
%e A213347   8 |  448  112
%e A213347   9 | 2016 1008 36
%t A213347 With[{q = 5}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 15}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* _Michael De Vlieger_, Nov 18 2019 *)
%o A213347 (PARI) See A213343; set thisq = 5
%Y A213347 Cf. A051288 (q=0), A213343 to A213346 (q=1 to 4), A213348 to A213352 (q=6 to 10).
%Y A213347 A054849 (first column), A004311 (row sums).
%K A213347 tabf,nonn
%O A213347 5,2
%A A213347 _Stanislav Sykora_, Jun 13 2012