OFFSET
5,1
COMMENTS
From Richard Stanley, Jan 30 2014: (Start)
The previous name "Number of partitions of a n-gon into (n-3) parts" was erroneous.
Cayley does not seem to have a combinatorial interpretation of this sequence. He just uses it as an auxiliary sequence, nor am I aware of a combinatorial interpretation in the literature.
(End)
First subdiagonal of the table of V(r,k) on page 240. The values V(11,8) = 24052, V(13,10)= 396800 and V(15,12)= 6547520 of the publication are replaced/corrected in the sequence.
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) = 2*binomial(2*n-5,n-5) = 2*A003516(n-3). - David Callan, Mar 30 2007
G.f. 64*x^5/((1+sqrt(1-4*x))^5*sqrt(1-4*x)). - R. J. Mathar, Nov 27 2011
a(n) ~ 4^n/(16*sqrt(Pi*n)). - Ilya Gutkovskiy, Apr 11 2017
PROG
(PARI) x='x+O('x^66); Vec(64*x^5/((1+sqrt(1-4*x))^5*sqrt(1-4*x))) \\ Joerg Arndt, Jan 30 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition corrected by Richard Stanley, Jan 30 2014
STATUS
approved