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

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

Offset: 6

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A002058, A002060.

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