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A054727 Number of forests of rooted trees with n nodes on a circle without crossing edges. 4
1, 2, 7, 33, 181, 1083, 6854, 45111, 305629, 2117283, 14929212, 106790500, 773035602, 5652275723, 41683912721, 309691336359, 2315772552485, 17415395593371, 131632335068744, 999423449413828 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

P. Flajolet and M. Noy, Analytic Combinatorics of Noncrossing Configurations, Discrete Math. 204 (1999), 203-229.

LINKS

Table of n, a(n) for n=1..20.

C. Banderier and D. Merlini, Lattice paths with an infinite set of jumps, FPSAC02, Melbourne, 2002.

F. Cazals, Combinatorics of Non-Crossing Configurations, Studies in Automatic Combinatorics, Volume II (1997).

Source

Philippe Flajolet, Enumeration of planar configurations in computational geometry

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 486, 502

FORMULA

add(binomial(n, j - 1)*binomial(3*n - 2*j - 1, n - j)/(2*n - j), j = 1 .. n)

G.f. A(x) satisfies 2*A(x)^2=x*(1-sqrt(1-4*A(x)))*(1-A(x)). [From Vladimir Kruchinin, Nov 25 2011]

MAPLE

ZZ:=[F, {F=Union(Epsilon, ZB), ZB=Prod(Z1, P), P=Sequence(B), B=Prod(P, Z1, P), Z1=Prod(Z, F)}, unlabeled]: seq(count(ZZ, size=n), n=1..20); - Zerinvary Lajos, Apr 22 2007

MATHEMATICA

a[n_] := (3*n-3)!/((n-1)!*(2*n-1)!)*HypergeometricPFQ[{1-2*n, 1-n, -n}, {3/2 - 3*n/2, 2 - 3*n/2}, -1/4]; Table[a[n], {n, 1, 20}] (* Jean-Fran├žois Alcover, Sep 05 2012, after formula *)

CROSSREFS

Cf. A006013.

Sequence in context: A162257 A214954 A055724 * A086618 A224769 A249636

Adjacent sequences:  A054724 A054725 A054726 * A054728 A054729 A054730

KEYWORD

nonn

AUTHOR

Philippe Flajolet, Apr 20 2000

STATUS

approved

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Last modified November 24 02:09 EST 2014. Contains 249867 sequences.