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

Author

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

Keywords

• easy
• nonn

References

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

Links

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

Crossrefs

Cf. A000312, A000108.

Programs

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);

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)