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

3, 32, 225, 1320, 7007, 34944, 167076, 775200, 3517470, 15690048, 69052555, 300638520, 1297398375, 5557977600, 23663585880, 100222246080, 422559514170, 1774647576000, 7427639542050, 30994292561232, 128989359164358

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

Table of n, a(n) for n=6..26.

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

N. J. A. Sloane

Status

approved