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