%I M3130 N1269 #37 Feb 04 2022 02:02:12
%S 3,32,225,1320,7007,34944,167076,775200,3517470,15690048,69052555,
%T 300638520,1297398375,5557977600,23663585880,100222246080,
%U 422559514170,1774647576000,7427639542050,30994292561232,128989359164358
%N Number of partitions of an n-gon into (n-4) parts.
%C Second subdiagonal of the table of values of V(r,k) on page 240.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A. Cayley, <a href="http://dx.doi.org/10.1112/plms/s1-22.1.237"> On the partitions of a polygon</a>, Proc. London Math. Soc., 22 (1891), 237-262
%H A. Cayley, <a href="http://www.hti.umich.edu/cgi/t/text/pageviewer-idx?sid=b88432273f115fb346725f1a42422e19&idno=abs3153.0013.001&c=umhistmath&cc=umhistmath&seq=110&view=image">On the partitions of a polygon</a>, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 13, pp. 93ff.
%F a(n) = (n-3) * binomial(2n-6,n). - _Gill Barequet_, Nov 09 2011
%F 9*n*(n-6)*a(n) + 2*(-17n^2+90n-133)*a(n-2) - 4*(n-4)(2n-9)*a(n-2) = 0. - _R. J. Mathar_, Nov 26 2011
%F G.f.: 64*x^6*(2*x+3*sqrt(1-4x))/( (1+sqrt(1-4x))^6 * (1-4x)^(3/2)). - _R. J. Mathar_, Nov 27 2011
%F a(n) ~ 4^n*sqrt(n)/(64*sqrt(Pi)). - _Ilya Gutkovskiy_, Apr 11 2017
%Y Cf. A002058, A002060.
%K nonn
%O 6,1
%A _N. J. A. Sloane_