OFFSET
1,3
COMMENTS
From Mohamed Sabba, Apr 24 2023: (Start)
The numerators of this sequence and denominators (A086117) appear in NMR and spin physics as half of the symmetry-constrained upper bound on polarization transfer in AXn spin-1/2 systems. For example:
(a) in AX3 and AX4 spin systems, the maximum achievable transfer from Xz to Az is 3/2 = (2*3/4).
(b) in AX5 and AX6 spin systems, the maximum achievable transfer from Xz to Az is 15/8 = (2*15/16).
Note that this is different from the related adiabatic polarization transfer bounds, given by A141244.
(End)
LINKS
Ole W. Sørensen, A universal bound on spin dynamics, Journal of Magnetic Resonance, 86:2 (1990) (equations 20 and 21)
Ole W. Sørensen, Polarization transfer experiments in high-resolution NMR spectroscopy, Progress in Nuclear Magnetic Resonance Spectroscopy, 21:6 (1989), (page 534)
Eric Weisstein's World of Mathematics, Random Walk 1-Dimensional
Eric Weisstein's World of Mathematics, Binomial Distribution
MATHEMATICA
Numerator[Table[If[OddQ[n], n!!/2/(n-1)!!, (n-1)!!/2/(n-2)!! ], {n, 50}]]
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Jul 10 2003
STATUS
approved