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 A002059 Number of partitions of a n-gon into (n-4) parts. (Formerly M3130 N1269) 3

%I M3130 N1269

%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 a 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&amp;idno=abs3153.0013.001&amp;c=umhistmath&amp;cc=umhistmath&amp;seq=110&amp;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_.

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Last modified February 22 06:04 EST 2019. Contains 320389 sequences. (Running on oeis4.)