%I #17 May 31 2018 04:41:06
%S 21,264,2134,14108,83072,453812,2352872,11740144,56894391,269476772,
%T 1253108594,5740109460,25966561036,116231267108,515605930368,
%U 2269542200416,9922528937450,43125192822720,186450920282476,802370755873080,3438559602598096,14680863523207304
%N Number of n-faced simplicial decompositions on a cylinder.
%H Juanjo Rué, <a href="https://doi.org/10.1016/j.disc.2010.06.023">Enumeration and limit laws of dissections on a cylinder</a>, Discrete Math., 310 (2010), 2519-2541.
%F The reference gives an explicit g.f.
%o (PARI)
%o acyl(m)={
%o my( x='x+O('x^(m+3)), Cx, Nx, Dx, Hx );
%o Cx = (1 - sqrt(1-4*x))/(2*x); /* g.f. of the Catalan numbers (A000108) */
%o Nx = ((-8*x^5+18*x^4-52*x^3+20*x^2+2*x-1)*Cx + (8*x^5-2*x^4+33*x^3-20*x^2-x+1));
%o Dx = (x*(1-4*x)^2);
%o Hx = Nx/Dx;
%o for(n=0, m, print1(polcoeff(Hx, n, 'x), ", "));
%o } /* _Michel Marcus_, Feb 06 2013 */
%K nonn
%O 6,1
%A _N. J. A. Sloane_, Aug 26 2010
%E More terms from _Michel Marcus_, Feb 06 2013