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

1, 16, 144, 9, 960, 180, 5280, 1980, 55, 25344, 15840, 1320, 109824, 102960, 17160, 286, 439296, 576576, 160160, 8008, 1647360, 2882880, 1201200, 120120, 1365, 5857280, 13178880, 7687680, 1281280, 43680, 19914752, 56010240

Offset

7,2

Comments

For a general discussion, please see A213343.

This a(n) is for septuple-quantum transitions (q = 7).

It lists the flattened triangle T(7;N,k) with rows N = 7,8,... and columns k = 0..floor((N-7)/2).

References

See A213343

Links

Stanislav Sykora, Table of n, a(n) for n = 7..2262

Stanislav Sykora, T(7;N,k) with rows N = 7..100 and columns k = 0..floor((N-7)/2)

Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.

Formula

Set q = 7 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-7)/2)
   7 |    1
   8 |   16
   9 |  144    9
  10 |  960  180
  11 | 5280 1980 55

Mathematica

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 *)

Prog

(PARI) See A213343; set thisq = 7

Crossrefs

Cf. A051288 (q=0), A213343 to A213348 (q=1 to 6), A213350 to A213352 (q=8 to 10).

Cf. A054851 (first column), A004313 (row sums).

Sequence in context: A232311 A048533 A303145 * A336239 A332105 A032444

Adjacent sequences: A213346 A213347 A213348 * A213350 A213351 A213352

Keyword

nonn,tabf

Author

Stanislav Sykora, Jun 13 2012

Status

approved