A191280 a(0)=1; for n>0, p2(n)+Sum(binomial(2*k,k)*p2(n-k)/2,k=1..n-1) where p2 = A002995, the number of unlabeled planar trees on n nodes.

1, 1, 2, 6, 18, 60, 210, 754, 2766, 10280, 38568, 145770, 554162, 2116568, 8115660, 31220672, 120442860, 465775226, 1805074882, 7008550224, 27257398714, 106166467074, 414068416752, 1616899329454, 6320798698322, 24734167234028, 96877398455260, 379765373701964, 1489867265555382, 5849164981941642, 22979031257945948

Offset: 0

Author

N. J. A. Sloane, May 29 2011

Keywords

• nonn

Links

• Seunghyun Seo and Heesung Shin, Two involutions on vertices of ordered trees

Crossrefs

Cf. A000108, A002995.

Programs

Maple

C:=n->binomial(2*n,n)/(n+1); # A000108
ch:=n->if n mod 2 = 1 then 1 else 0; fi;
p2:=n->(1/(2*n)*add(numtheory[phi](n/d)*binomial(2*d,d), d in divisors(n))) - C(n)/2 +(1/2)*ch(n)*C((n-1)/2); # A002995
a:=n->p2(n)+add(binomial(2*k,k)*p2(n-k)/2,k=1..n-1); [valid for n >= 1]