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A213352 10-quantum transitions in systems of N >= 10 spin 1/2 particles, in columns by combination indices.

%I A213352 #23 Nov 21 2019 00:10:00
%S A213352 1,22,264,12,2288,312,16016,4368,91,96096,43680,2730,512512,349440,
%T A213352 43680,560,2489344,2376192,495040,19040,11202048,14257152,4455360,
%U A213352 342720,3060,47297536,77395968,33860736,4341120,116280,189190144,386979840,225738240,43411200
%N A213352 10-quantum transitions in systems of N >= 10 spin 1/2 particles, in columns by combination indices.
%C A213352 For a general discussion, please see A213343.
%C A213352 This a(n) is for decuple-quantum transitions (q = 10).
%C A213352 It lists the flattened triangle T(10;N,k) with rows N = 10,11,... and columns k = 0..floor((N-10)/2).
%D A213352 See A213343.
%H A213352 Stanislav Sykora, <a href="/A213352/b213352.txt">Table of n, a(n) for n = 10..2125</a>
%H A213352 Stanislav Sykora, <a href="/A213352/a213352.txt">T(10;N,k) with rows N=10..100 and columns k=0..floor((N-10)/2)</a>
%H A213352 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 A213352 Set q = 10 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).
%e A213352 Starting rows of the triangle:
%e A213352    N | k = 0, 1, ..., floor((N-10)/2)
%e A213352   ---+-------------------------------
%e A213352   10 |     1
%e A213352   11 |    22
%e A213352   12 |   264   12
%e A213352   13 |  2288  312
%e A213352   14 | 16016 4368 91
%t A213352 With[{q = 10}, 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 A213352 (PARI) See A213343; set thisq = 10
%Y A213352 Cf. A051288 (q=0), A213343 to A213351 (q=1 to 9).
%Y A213352 Cf. A172242 (first column), A004316 (row sums).
%K A213352 nonn,tabl
%O A213352 10,2
%A A213352 _Stanislav Sykora_, Jun 13 2012