A071214 Number of labeled ordered trees with n nodes such that the root is smaller than all its children.

1, 5, 46, 614, 10716, 230712, 5903472, 174942000, 5890370400, 222069752640, 9265980286080, 423888544154880, 21094789126924800, 1134492559101619200, 65567415318776985600, 4052502049455940147200, 266725354163752808755200, 18624661769541550593024000

Offset

2,2

References

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

Links

Table of n, a(n) for n=2..19.

C. Chauve, S. Dulucq and O. Guibert, Enumeration of some labelled trees, FPSAC 2000, pp. 146-157. 2000.

Formula

From Vladimir Kruchinin, Jun 02 2016: (Start)

E.g.f.: -[(log(1-x*C(x)))/C(x)]', where C(x) is g.f. of Catalan numbers (A000108).

a(n) = ((n+1)!*Sum_{k=1..n} ((k*binomial(2*n-k-1,n-k))/(k+1)))/n. (End)

Maple

a:= n -> ((2*n-2)! / (n-1)!) - sum((n+k-1)! / ((n-k-1)*k!), k=0 .. n-2):
seq(a(n), n=2..22);

Crossrefs

Cf. A000312, A000108.

Sequence in context: A167559 A367154 A121631 * A052873 A052894 A363355

Adjacent sequences: A071211 A071212 A071213 * A071215 A071216 A071217

Keyword

easy,nonn

Author

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

Status

approved