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

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

Author

Stanislav Sykora, Jun 13 2012

Keywords

• nonn
• tabl

Comments

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).

Examples

			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
		

References

• See A213343

Links

• 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.

Crossrefs

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

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

Programs

Mathematica

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

Formula

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