A071213 Number of labeled planar trees with n nodes such that the root is smaller than all its children.

1, 4, 34, 436, 7428, 157368, 3980688, 116949600, 3911421600, 146673662400, 6093249563520, 277729608280320, 13778539159795200, 739059210587980800, 42615627311477606400, 2628646012982829772800, 172704619437756321484800

Offset

2,2

Links

Table of n, a(n) for n=2..18.

C. Chauve, S. Dulucq and O. Guibert, Enumeration of some labeled trees, research report RR-1226-99, LaBRI, Bordeaux I University, 1999.

Formula

E.g.f.: F(C(x))+x*[F(C(x))]', where C(x)/x is g.f. of Catalan numbers (A000108), F(x)=1+log(1-x)/x-log(1-x). - Vladimir Kruchinin, Mar 23 2016

Maple

n -> 2 * sum((n-1) * (n-2+k)! / (k! * (n-1-k)), k=0 .. n-2) - ((2*n-3)! / (n-2)!);

Prog

(Maxima)
C(x):=(1-sqrt(1-4*x))/(2);
F(x):=1+log(1-x)/x-log(1-x);
makelist(n!*coeff(taylor(F(C(x))+x*diff(F(C(x)), x), x, 0, 15), x, n), n, 1, 15); /*Vladimir Kruchinin, Mar 23 2016 */

Crossrefs

Cf. A000108, A000312, A033184.

Sequence in context: A309170 A338163 A052630 * A052629 A151919 A277637

Adjacent sequences: A071210 A071211 A071212 * A071214 A071215 A071216

Keyword

easy,nonn

Author

Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002

Status

approved