A213350 -id:A213350 - cp's OEIS frontend

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

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).

A213351 9-quantum transitions in systems of N >= 9 spin 1/2 particles, in columns by combination indices.

Original entry on oeis.org

1, 20, 220, 11, 1760, 264, 11440, 3432, 78, 64064, 32032, 2184, 320320, 240240, 32760, 455, 1464320, 1537536, 349440, 14560, 6223360, 8712704, 2970240, 247520, 2380, 24893440, 44808192, 21385728, 2970240, 85680, 94595072, 212838912, 135442944, 28217280

Offset: 9

Stanislav Sykora, Jun 13 2012

For a general discussion, please see A213343.
This a(n) is for nonuple-quantum transitions (q = 9).
It lists the flattened triangle T(9;N,k) with rows N = 9,10,... and columns k = floor((N-9)/2).

			Starting rows of the triangle:
   N | k = 0, 1, ..., floor((N-9)/2)
  ---+------------------------------
   9 | 1
  10 | 20
  11 | 220 11
  12 | 1760 264
  13 | 11440 3432 78

See A213343

Stanislav Sykora, Table of n, a(n) for n = 9..2170
Stanislav Sykora, T(9;N,k) with rows N = 9..100 and columns k = 0..floor((N-9)/2)
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.

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

Cf. A140354 (first column,with offset 9), A004315 (row sums).

With[{q = 9}, 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 = 9
```

Set q = 9 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).

cp's OEIS Frontend

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

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