A213348 -id:A213348 - cp's OEIS frontend

A213347 5-quantum transitions in systems of N>=5 spin 1/2 particles, in columns by combination indices.

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

Stanislav Sykora, Jun 13 2012

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).

			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

See A213343

Stanislav Sykora, Table of n, a(n) for n = 5..2356
Stanislav Sykora, T(5;N,k) with rows N=5,..,100 and columns k=0,..,floor((N-5)/2)
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.

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

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

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 *)

PARI
```
See A213343; set thisq = 5
```

Set q = 5 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).

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

Original entry on oeis.org

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

Stanislav Sykora, Jun 13 2012

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).

			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

See A213343

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.

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).

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 *)

PARI
```
See A213343; set thisq = 7
```

Set q = 7 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).

cp's OEIS Frontend

A213347 5-quantum transitions in systems of N>=5 spin 1/2 particles, in columns by combination indices.

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