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A052510 Number of labeled planar binary trees with n elements (external nodes or internal nodes). 2
1, 6, 240, 25200, 5080320, 1676505600, 821966745600, 560992303872000, 508633022177280000, 591438478187741184000, 858123464716031754240000, 1519736656012092236759040000, 3226517823533365056503808000000, 8089341114715793820234547200000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..14.

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(arcsec(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);

MATHEMATICA

nn=20; f[x_]:=Sum[a[n]x^n/n!, {n, 0, nn}]; s=SolveAlways[0==Series[f[x]-x(1+f[x]^2), {x, 0, nn}], x]; Select[Flatten[Table[a[n], {n, 0, nn}]/.s], #>0&]  (* Geoffrey Critzer, Mar 23 2013 *)

CROSSREFS

Equals 2^(n-1) * A036770(n).

Cf. A101921.

Sequence in context: A172965 A002022 A065948 * A234633 A137892 A064382

Adjacent sequences:  A052507 A052508 A052509 * A052511 A052512 A052513

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

STATUS

approved

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Last modified October 16 05:44 EDT 2018. Contains 316259 sequences. (Running on oeis4.)