%I #22 Nov 21 2019 00:09:39

%S 1,16,144,9,960,180,5280,1980,55,25344,15840,1320,109824,102960,17160,

%T 286,439296,576576,160160,8008,1647360,2882880,1201200,120120,1365,

%U 5857280,13178880,7687680,1281280,43680,19914752,56010240

%N 7-quantum transitions in systems of N >= 7 spin 1/2 particles, in columns by combination indices.

%C For a general discussion, please see A213343.

%C This a(n) is for septuple-quantum transitions (q = 7).

%C It lists the flattened triangle T(7;N,k) with rows N = 7,8,... and columns k = 0..floor((N-7)/2).

%D See A213343

%H Stanislav Sykora, <a href="/A213349/b213349.txt">Table of n, a(n) for n = 7..2262</a>

%H Stanislav Sykora, <a href="/A213349/a213349.txt">T(7;N,k) with rows N = 7..100 and columns k = 0..floor((N-7)/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 = 7 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-7)/2)

%e 7 | 1

%e 8 | 16

%e 9 | 144 9

%e 10 | 960 180

%e 11 | 5280 1980 55

%t With[{q = 7}, 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 (PARI) See A213343; set thisq = 7

%Y Cf. A051288 (q=0), A213343 to A213348 (q=1 to 6), A213350 to A213352 (q=8 to 10).

%Y Cf. A054851 (first column), A004313 (row sums).

%K nonn,tabf

%O 7,2

%A _Stanislav Sykora_, Jun 13 2012