cp's OEIS Frontend

A213349 7-quantum transitions in systems of N >= 7 spin 1/2 particles, in columns by combination indices.

%I A213349 #22 Nov 21 2019 00:09:39
%S A213349 1,16,144,9,960,180,5280,1980,55,25344,15840,1320,109824,102960,17160,
%T A213349 286,439296,576576,160160,8008,1647360,2882880,1201200,120120,1365,
%U A213349 5857280,13178880,7687680,1281280,43680,19914752,56010240
%N A213349 7-quantum transitions in systems of N >= 7 spin 1/2 particles, in columns by combination indices.
%C A213349 For a general discussion, please see A213343.
%C A213349 This a(n) is for septuple-quantum transitions (q = 7).
%C A213349 It lists the flattened triangle T(7;N,k) with rows N = 7,8,... and columns k = 0..floor((N-7)/2).
%D A213349 See A213343
%H A213349 Stanislav Sykora, <a href="/A213349/b213349.txt">Table of n, a(n) for n = 7..2262</a>
%H A213349 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 A213349 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 A213349 Set q = 7 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).
%e A213349 Starting rows of the triangle:
%e A213349    N | k = 0, 1, ..., floor((N-7)/2)
%e A213349    7 |    1
%e A213349    8 |   16
%e A213349    9 |  144    9
%e A213349   10 |  960  180
%e A213349   11 | 5280 1980 55
%t A213349 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 A213349 (PARI) See A213343; set thisq = 7
%Y A213349 Cf. A051288 (q=0), A213343 to A213348 (q=1 to 6), A213350 to A213352 (q=8 to 10).
%Y A213349 Cf. A054851 (first column), A004313 (row sums).
%K A213349 nonn,tabf
%O A213349 7,2
%A A213349 _Stanislav Sykora_, Jun 13 2012