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A213348 6-quantum transitions in systems of N >= 6 spin 1/2 particles, in columns by combination indices.

%I A213348 #26 Nov 21 2019 00:09:32
%S A213348 1,14,112,8,672,144,3360,1440,45,14784,10560,990,59136,63360,11880,
%T A213348 220,219648,329472,102960,5720,768768,1537536,720720,80080,1001,
%U A213348 2562560,6589440,4324320,800800,30030,8200192,26357760,23063040
%N A213348 6-quantum transitions in systems of N >= 6 spin 1/2 particles, in columns by combination indices.
%C A213348 For a general discussion, please see A213343.
%C A213348 This a(n) is for sextuple-quantum transitions (q = 6).
%C A213348 It lists the flattened triangle T(6;N,k) with rows N = 6,7,... and columns k = 0..floor((N-6)/2).
%D A213348 See A213343
%H A213348 Stanislav Sykora, <a href="/A213348/b213348.txt">Table of n, a(n) for n = 6..2309</a>
%H A213348 Stanislav Sykora, <a href="/A213348/a213348.txt">T(6;N,k) with rows N = 6..100 and columns k = 0..floor((N-6)/2)</a>
%H A213348 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 A213348 Set q = 6 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).
%e A213348 Starting rows of the triangle:
%e A213348    N | k = 0, 1, ..., floor((N-6)/2)
%e A213348    6 |    1
%e A213348    7 |   14
%e A213348    8 |  112    8
%e A213348    9 |  672  144
%e A213348   10 | 3360 1440 45
%t A213348 With[{q = 6}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, q, q + 10}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* _Michael De Vlieger_, Nov 20 2019 *)
%o A213348 (PARI) See A213343; set thisq = 6
%Y A213348 Cf. A051288 (q=0), A213343 to A213347 (q=1 to 5), A213349 to A213352 (q=7 to 10).
%Y A213348 Cf. A002409 (first column, with offset 6), A004312 (row sums).
%K A213348 nonn,tabf
%O A213348 6,2
%A A213348 _Stanislav Sykora_, Jun 13 2012