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 A002059 Number of partitions of an n-gon into (n-4) parts. (Formerly M3130 N1269) 3
 3, 32, 225, 1320, 7007, 34944, 167076, 775200, 3517470, 15690048, 69052555, 300638520, 1297398375, 5557977600, 23663585880, 100222246080, 422559514170, 1774647576000, 7427639542050, 30994292561232, 128989359164358 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,1 COMMENTS Second subdiagonal of the table of values of V(r,k) on page 240. REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS A. Cayley, On the partitions of a polygon, Proc. London Math. Soc., 22 (1891), 237-262 A. Cayley, On the partitions of a polygon, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 13, pp. 93ff. FORMULA a(n) = (n-3) * binomial(2n-6,n). - Gill Barequet, Nov 09 2011 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 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 a(n) ~ 4^n*sqrt(n)/(64*sqrt(Pi)). - Ilya Gutkovskiy, Apr 11 2017 CROSSREFS Cf. A002058, A002060. Sequence in context: A183457 A322234 A264574 * A028447 A081012 A187919 Adjacent sequences:  A002056 A002057 A002058 * A002060 A002061 A002062 KEYWORD nonn AUTHOR STATUS approved

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Last modified July 7 02:44 EDT 2022. Contains 355141 sequences. (Running on oeis4.)