A213347 - OEIS

%I #20 Nov 18 2019 22:07:07

%S 1,12,84,7,448,112,2016,1008,36,8064,6720,720,29568,36960,7920,165,

%T 101376,177408,63360,3960,329472,768768,411840,51480,715,1025024,

%U 3075072,2306304,480480,20020,3075072,11531520,11531520

%N 5-quantum transitions in systems of N>=5 spin 1/2 particles, in columns by combination indices.

%C For a general discussion, please see A213343.

%C This a(n) is for quintuple-quantum transitions (q = 5).

%C It lists the flattened triangle T(5;N,k) with rows N = 5,6,... and columns N, k = 0..floor((N-5)/2).

%D See A213343

%H Stanislav Sykora, <a href="/A213347/b213347.txt">Table of n, a(n) for n = 5..2356</a>

%H Stanislav Sykora, <a href="/A213347/a213347.txt">T(5;N,k) with rows N=5,..,100 and columns k=0,..,floor((N-5)/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 = 5 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-5)/2)

%e   5 |    1

%e   6 |   12

%e   7 |   84    7

%e   8 |  448  112

%e   9 | 2016 1008 36

%t With[{q = 5}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 15}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* _Michael De Vlieger_, Nov 18 2019 *)

%o (PARI) See A213343; set thisq = 5

%Y Cf. A051288 (q=0), A213343 to A213346 (q=1 to 4), A213348 to A213352 (q=6 to 10).

%Y A054849 (first column), A004311 (row sums).

%K tabf,nonn

%O 5,2

%A _Stanislav Sykora_, Jun 13 2012