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A213350
8-quantum transitions in systems of N >= 8 spin 1/2 particles, in columns by combination indices.
3
1, 18, 180, 10, 1320, 220, 7920, 2640, 66, 41184, 22880, 1716, 192192, 160160, 24024, 364, 823680, 960960, 240240, 10920, 3294720, 5125120, 1921920, 174720, 1820, 12446720, 24893440, 13069056, 1980160, 61880, 44808192, 112020480
OFFSET
8,2
COMMENTS
For a general discussion, please see A213343.
This a(n) is for octuple-quantum transitions (q = 8).
It lists the flattened triangle T(8;N,k) with rows N = 8,9,... and columns k = 0..floor((N-8)/2).
REFERENCES
LINKS
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
FORMULA
Set q = 8 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-8)/2)
---+------------------------------
8 | 1
9 | 18
10 | 180 10
11 | 1320 220
12 | 7920 2640 66
MATHEMATICA
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 *)
PROG
(PARI) See A213343; set thisq = 8
CROSSREFS
Cf. A051288 (q=0), A213343 to A213349 (q=1 to 7), A213351 (q=9), A213352 (q= 10).
Cf. A140325 (first row, with offset 8), A004314 (row sums).
Sequence in context: A321951 A227023 A239581 * A052507 A071910 A121038
KEYWORD
nonn,tabl
AUTHOR
Stanislav Sykora, Jun 13 2012
STATUS
approved