|
Search: id:A001761
|
|
|
| A001761 |
|
a(n) = (2*n)!/(n+1)!.
(Formerly M3635 N1478)
|
|
+0
13
|
|
| 1, 1, 4, 30, 336, 5040, 95040, 2162160, 57657600, 1764322560, 60949324800, 2346549004800, 99638080819200, 4626053752320000, 233153109116928000, 12677700308232960000, 739781100339240960000, 46113021921146019840000
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Number of dissections of a disk.
a(n+1) is the number of labeled incomplete ternary trees on n vertices in which each left and middle child have a larger label than their parent. - Brian Drake (bdrake(AT)brandeis.edu), Jul 28 2008
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. W. Beineke and R. E. Pippert, Enumerating labeled k-dimensional trees and ball dissections, pp. 12-26 of Proceedings of Second Chapel Hill Conference on Combinatorial Mathematics and Its Applications, University of North Carolina, Chapel Hill, 1970. Reprinted in Math. Annalen, 191 (1971), 87-98.
|
|
LINKS
|
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 80
K. A. Penson and J.-M. Sixdeniers, Integral Representations of Catalan and Related Numbers, J. Integer Sequences, 4 (2001), #01.2.5.
K. A. Penson and A. I. Solomon, Coherent states from combinatorial sequences.
|
|
FORMULA
|
a(n+2) = sum(A038455(n, m), m=1..n), n >= 1 - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
E.g.f. for this sequence = o.g.f. for A000108. - Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 07 2001
Integral representation as the moment of a positive function on the positive half-axis: in Maple notation a(n)=int(x^n*(-1/2+exp(-x/4)/sqrt(Pi*x)+erf(sqrt(x)/2)/2), x=0..infinity), n=0, 1... This representation is unique. - Karol.A. Penson (penson(AT)lptl.jussieu.fr), Aug 21 2001
n!*binomial(2*n,n)/(n+1) or A000108*n! - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2006
|
|
MAPLE
|
seq(mul((n+k), k=2..n), n=0..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 15 2008
with(finance):seq(mul(cashflows([n, k, 2], 0), k=1..n), n=-1..22); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
|
|
PROGRAM
|
(Mupad) combinat::catalan(n)*n! $ n = 0..17; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 15 2007
|
|
CROSSREFS
|
Sequence in context: A128329 A006149 A121413 this_sequence A099712 A052316 A089918
Adjacent sequences: A001758 A001759 A001760 this_sequence A001762 A001763 A001764
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
