Table of n, a(n) for n=5..13.
C. A. Athanasiadis, J. A. De Loera, V. Reiner and F. Santos, Fiber polytopes for the projections between cyclic polytopes, European Journal of Combinatorics, Volume: 21, Issue: 1, 2000, pp. 19 - 47.
M. Azaola and F. Santos, The number of triangulations of the cyclic polytope C(n,n-4), Discrete Comput. Geom., 27 (2002), 29-48.
Michael Joswig, Lars Kastner, New counts for the number of triangulations of cyclic polytopes, arXiv:1804.08029 [math.CO], 2018.
J. Rambau, TOPCOM
J. Rambau and V. Reiner, A survey of the higher Stasheff-Tamari orders, in Progress in Mathematics, Vol. 299, Birkhauser 2012.
J. Rambau and F. Santos, The Baues problem for cyclic polytopes I, In "Special issue on Combinatorics of convex polytopes" (K. Fukuda and G. M. Ziegler, eds.), European J. Combin. 21:1 (2000), 65-83.