A213351 -id:A213351 - cp's OEIS frontend

A213352 10-quantum transitions in systems of N >= 10 spin 1/2 particles, in columns by combination indices.

1, 22, 264, 12, 2288, 312, 16016, 4368, 91, 96096, 43680, 2730, 512512, 349440, 43680, 560, 2489344, 2376192, 495040, 19040, 11202048, 14257152, 4455360, 342720, 3060, 47297536, 77395968, 33860736, 4341120, 116280, 189190144, 386979840, 225738240, 43411200

Offset: 10

Stanislav Sykora, Jun 13 2012

For a general discussion, please see A213343.
This a(n) is for decuple-quantum transitions (q = 10).
It lists the flattened triangle T(10;N,k) with rows N = 10,11,... and columns k = 0..floor((N-10)/2).

			Starting rows of the triangle:
   N | k = 0, 1, ..., floor((N-10)/2)
  ---+-------------------------------
  10 |     1
  11 |    22
  12 |   264   12
  13 |  2288  312
  14 | 16016 4368 91

See A213343.

Stanislav Sykora, Table of n, a(n) for n = 10..2125
Stanislav Sykora, T(10;N,k) with rows N=10..100 and columns k=0..floor((N-10)/2)
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.

Cf. A051288 (q=0), A213343 to A213351 (q=1 to 9).

Cf. A172242 (first column), A004316 (row sums).

With[{q = 10}, 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 = 10
```

Set q = 10 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).

A213350 8-quantum transitions in systems of N >= 8 spin 1/2 particles, in columns by combination indices.

Original entry on oeis.org

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

Stanislav Sykora, Jun 13 2012

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).

			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

See A213343

Stanislav Sykora, Table of n, a(n) for n = 8..2216
Stanislav Sykora, T(8;N,k) with rows N = 8..100 and columns k = 0..floor((N-8)/2)
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.

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).

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 *)

PARI
```
See A213343; set thisq = 8
```

Set q = 8 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k)

cp's OEIS Frontend

A213352 10-quantum transitions in systems of N >= 10 spin 1/2 particles, in columns by combination indices.

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