cp's OEIS Frontend

A213350 8-quantum transitions in systems of N >= 8 spin 1/2 particles, in columns by combination indices.

%I A213350 #18 Nov 21 2019 00:09:46
%S A213350 1,18,180,10,1320,220,7920,2640,66,41184,22880,1716,192192,160160,
%T A213350 24024,364,823680,960960,240240,10920,3294720,5125120,1921920,174720,
%U A213350 1820,12446720,24893440,13069056,1980160,61880,44808192,112020480
%N A213350 8-quantum transitions in systems of N >= 8 spin 1/2 particles, in columns by combination indices.
%C A213350 For a general discussion, please see A213343.
%C A213350 This a(n) is for octuple-quantum transitions (q = 8).
%C A213350 It lists the flattened triangle T(8;N,k) with rows N = 8,9,... and columns k = 0..floor((N-8)/2).
%D A213350 See A213343
%H A213350 Stanislav Sykora, <a href="/A213350/b213350.txt">Table of n, a(n) for n = 8..2216</a>
%H A213350 Stanislav Sykora, <a href="/A213350/a213350.txt">T(8;N,k) with rows N = 8..100 and columns k = 0..floor((N-8)/2)</a>
%H A213350 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 A213350 Set q = 8 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k)
%e A213350 Starting rows of the triangle:
%e A213350    N | k = 0, 1, ..., floor((N-8)/2)
%e A213350   ---+------------------------------
%e A213350    8 |    1
%e A213350    9 |   18
%e A213350   10 |  180   10
%e A213350   11 | 1320  220
%e A213350   12 | 7920 2640 66
%t A213350 With[{q = 8}, 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 A213350 (PARI) See A213343; set thisq = 8
%Y A213350 Cf. A051288 (q=0), A213343 to A213349 (q=1 to 7), A213351 (q=9), A213352 (q= 10).
%Y A213350 Cf. A140325 (first row, with offset 8), A004314 (row sums).
%K A213350 nonn,tabl
%O A213350 8,2
%A A213350 _Stanislav Sykora_, Jun 13 2012