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A213347
5-quantum transitions in systems of N>=5 spin 1/2 particles, in columns by combination indices.
3
1, 12, 84, 7, 448, 112, 2016, 1008, 36, 8064, 6720, 720, 29568, 36960, 7920, 165, 101376, 177408, 63360, 3960, 329472, 768768, 411840, 51480, 715, 1025024, 3075072, 2306304, 480480, 20020, 3075072, 11531520, 11531520
OFFSET
5,2
COMMENTS
For a general discussion, please see A213343.
This a(n) is for quintuple-quantum transitions (q = 5).
It lists the flattened triangle T(5;N,k) with rows N = 5,6,... and columns N, k = 0..floor((N-5)/2).
REFERENCES
LINKS
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
FORMULA
Set q = 5 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).
EXAMPLE
Starting rows of the triangle:
N | k = 0, 1, ..., floor((N-5)/2)
5 | 1
6 | 12
7 | 84 7
8 | 448 112
9 | 2016 1008 36
MATHEMATICA
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 *)
PROG
(PARI) See A213343; set thisq = 5
CROSSREFS
Cf. A051288 (q=0), A213343 to A213346 (q=1 to 4), A213348 to A213352 (q=6 to 10).
A054849 (first column), A004311 (row sums).
Sequence in context: A275743 A026949 A165127 * A075476 A298977 A213784
KEYWORD
tabf,nonn
AUTHOR
Stanislav Sykora, Jun 13 2012
STATUS
approved