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 A071214 Number of labeled ordered trees with n nodes such that the root is smaller than all its children. 0
 1, 5, 46, 614, 10716, 230712, 5903472, 174942000, 5890370400, 222069752640, 9265980286080, 423888544154880, 21094789126924800, 1134492559101619200, 65567415318776985600, 4052502049455940147200, 266725354163752808755200, 18624661769541550593024000 (list; graph; refs; listen; history; text; internal format)
 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 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: A159608 A167559 A121631 * A052873 A052894 A292408 Adjacent sequences:  A071211 A071212 A071213 * A071215 A071216 A071217 KEYWORD easy,nonn AUTHOR Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002 STATUS approved

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Last modified May 24 22:34 EDT 2022. Contains 354047 sequences. (Running on oeis4.)