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%I #19 Nov 21 2019 00:09:52
%S 1,20,220,11,1760,264,11440,3432,78,64064,32032,2184,320320,240240,
%T 32760,455,1464320,1537536,349440,14560,6223360,8712704,2970240,
%U 247520,2380,24893440,44808192,21385728,2970240,85680,94595072,212838912,135442944,28217280
%N 9-quantum transitions in systems of N >= 9 spin 1/2 particles, in columns by combination indices.
%C For a general discussion, please see A213343.
%C This a(n) is for nonuple-quantum transitions (q = 9).
%C It lists the flattened triangle T(9;N,k) with rows N = 9,10,... and columns k = floor((N-9)/2).
%D See A213343
%H Stanislav Sykora, <a href="/A213351/b213351.txt">Table of n, a(n) for n = 9..2170</a>
%H Stanislav Sykora, <a href="/A213351/a213351.txt">T(9;N,k) with rows N = 9..100 and columns k = 0..floor((N-9)/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 = 9 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-9)/2)
%e ---+------------------------------
%e 9 | 1
%e 10 | 20
%e 11 | 220 11
%e 12 | 1760 264
%e 13 | 11440 3432 78
%t With[{q = 9}, 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 = 9
%Y Cf. A051288 (q=0), A213343 to A213350 (q=1 to 8), A213352 (q= 10).
%Y Cf. A140354 (first column,with offset 9), A004315 (row sums).
%K nonn,tabl
%O 9,2
%A _Stanislav Sykora_, Jun 13 2012