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A213351 9-quantum transitions in systems of N >= 9 spin 1/2 particles, in columns by combination indices.

%I A213351 #22 Aug 18 2025 18:15:04
%S A213351 1,20,220,11,1760,264,11440,3432,78,64064,32032,2184,320320,240240,
%T A213351 32760,455,1464320,1537536,349440,14560,6223360,8712704,2970240,
%U A213351 247520,2380,24893440,44808192,21385728,2970240,85680,94595072,212838912,135442944,28217280
%N A213351 9-quantum transitions in systems of N >= 9 spin 1/2 particles, in columns by combination indices.
%C A213351 For a general discussion, please see A213343.
%C A213351 This a(n) is for nonuple-quantum transitions (q = 9).
%C A213351 It lists the flattened triangle T(9;N,k) with rows N = 9,10,... and columns k = floor((N-9)/2).
%D A213351 See A213343
%H A213351 Stanislav Sykora, <a href="/A213351/b213351.txt">Table of n, a(n) for n = 9..2170</a>
%H A213351 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 A213351 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 A213351 Set q = 9 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).
%e A213351 Starting rows of the triangle:
%e A213351    N | k = 0, 1, ..., floor((N-9)/2)
%e A213351   ---+------------------------------
%e A213351    9 | 1
%e A213351   10 | 20
%e A213351   11 | 220 11
%e A213351   12 | 1760 264
%e A213351   13 | 11440 3432 78
%t A213351 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 A213351 (PARI) \\ See A213343; set thisq = 9
%Y A213351 Cf. A051288 (q=0), A213343 to A213350 (q=1 to 8), A213352 (q= 10).
%Y A213351 Cf. A140354 (first column,with offset 9), A004315 (row sums).
%K A213351 nonn,tabl
%O A213351 9,2
%A A213351 _Stanislav Sykora_, Jun 13 2012