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A213346 4-quantum transitions in systems of N>=4 spin 1/2 particles, in columns by combination indices.

%I A213346 #20 Nov 18 2019 22:07:01
%S A213346 1,10,60,6,280,84,1120,672,28,4032,4032,504,13440,20160,5040,120,
%T A213346 42240,88704,36960,2640,126720,354816,221760,31680,495,366080,1317888,
%U A213346 1153152,274560,12870,1025024,4612608,5381376,1921920,180180,2002
%N A213346 4-quantum transitions in systems of N>=4 spin 1/2 particles, in columns by combination indices.
%C A213346 For a general discussion, please see A213343.
%C A213346 This a(n) is for quadruple-quantum transitions (q = 4).
%C A213346 It lists the flattened triangle T(4;N,k) with rows N = 4,5,... and columns k = 0..floor((N-4)/2).
%D A213346 See A213343.
%H A213346 Stanislav Sykora, <a href="/A213346/b213346.txt">Table of n, a(n) for n = 4..2404</a>
%H A213346 Stanislav Sykora, <a href="/A213346/a213346.txt">T(4;N,k) with rows N=4,..,100 and columns k=0,..,floor((N-4)/2)</a>
%H A213346 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 A213346 Set q = 4 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k)
%e A213346 Starting rows of the triangle:
%e A213346   N | k = 0, 1, ..., floor((N-4)/2)
%e A213346   4 |    1
%e A213346   5 |   10
%e A213346   6 |   60   6
%e A213346   7 |  280  84
%e A213346   8 | 1120 672 28
%t A213346 With[{q = 4}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 14}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* _Michael De Vlieger_, Nov 18 2019 *)
%o A213346 (PARI) See A213343; set thisq = 4
%Y A213346 Cf. A051288 (q=0), A213343 to A213345 (q=1 to 3), A213347 to A213352 (q=5 to 10).
%Y A213346 Cf. A003472 (first column), A004310 (row sums).
%K A213346 tabl,nonn
%O A213346 4,2
%A A213346 _Stanislav Sykora_, Jun 12 2012