

A108225


a(0) = 0, a(1) = 2; for n >= 2, a(n) = (a(n1) + a(n2))*(a(n1)  a(n2) + 1)/2.


2



0, 2, 3, 5, 12, 68, 2280, 2598062, 3374961778893, 5695183504492614029263280, 16217557574922386301420536972254869595782763547562
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OFFSET

0,2


COMMENTS

From a posting by Antreas P. Hatzipolakis to the Yahoo news group "Hyacinthos", circa Jun 10 2005.
a(n) for n>0 gives the rank of the unlabeled binary rooted tree, among those with n+1 leaves, that has the largest rank according to the bijection of Colijn and Plazzotta (2018) between unlabeled binary rooted trees and positive integers.  Noah A Rosenberg, Jun 03 2022


LINKS



FORMULA



MAPLE

F:=proc(n) option remember; if n <= 1 then RETURN(2*n) fi; (F(n1)+F(n2))*(F(n1)F(n2)+1)/2; end;
a[ 2]:=2:a[ 1]:=0:a[0]:=1:for n from 1 to 50 do a[n]:=binomial(a[n1]+2, 2) od: seq(a[n]+2, n=2..8); # Zerinvary Lajos, Jun 08 2007


MATHEMATICA

RecurrenceTable[{a[0]==0, a[1]==2, a[n]==(a[n1]+a[n2])(a[n1] a[n2]+1)/2}, a[n], {n, 15}] (* Harvey P. Dale, Jun 09 2011 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



