|
Search: id:A052510
|
|
|
| A052510 |
|
Number of labeled planar binary trees with n elements (external nodes or internal nodes). |
|
+0
3
|
|
| 1, 6, 240, 25200, 5080320, 1676505600, 821966745600, 560992303872000, 508633022177280000, 591438478187741184000
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 54
|
|
FORMULA
|
E.g.f.: (1/2)/x*(1-(1-4*x^2)^(1/2))
Recurrence: {a(1)=1, a(2)=0, (-4*n^3-12*n^2-8*n)*a(n)+(n+3)*a(n+2), a(3)=6}
a(n) = (2n-1)/n * ( (2(n-1))! / (n-1)! )^2 - Travis Kowalski (kowalski(AT)euclid.UCSD.Edu), Dec 15, 2000
I*sin(asec(2x)) = -1/2x + x + 6x^3/3! + 240x^5/5! + 25200x^7/7! +...
|
|
MAPLE
|
spec := [S, {S=Union(Z, Prod(Z, S, S))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
|
|
CROSSREFS
|
Equals 2^(n-1) * A036770(n). Cf. A101921.
Sequence in context: A077231 A002022 A065948 this_sequence A137892 A064382 A080358
Adjacent sequences: A052507 A052508 A052509 this_sequence A052511 A052512 A052513
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
|
Search completed in 0.002 seconds
|
