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A002059
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Number of partitions of a n-gon into (n-4) parts.
(Formerly M3130 N1269)
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2
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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; internal format)
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OFFSET
| 6,1
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COMMENTS
| Second subdiagonal of the table of values of V(r,k) on page 240.
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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).
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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.
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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
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CROSSREFS
| Cf. A002058, A002060.
Sequence in context: A119940 A004256 A183457 * A028447 A081012 A187919
Adjacent sequences: A002056 A002057 A002058 * A002060 A002061 A002062
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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