A200793 The number of forests on n nodes of rooted labeled binary trees (each node has degree <=2).

1, 1, 3, 16, 121, 1191, 14461, 209098, 3510921, 67175461, 1443249271, 34412298636, 901898694313, 25775139581491, 797824620178041, 26592701386533766, 949705032131053201, 36181186751341438473, 1464760631695118359051, 62798619981256526628136

Offset: 0

Author

Geoffrey Critzer, Nov 22 2011

Keywords

• nonn

Programs

Mathematica

u=(1-x-((x-1)^2-2x^2)^(1/2))/x; Range[0,20]! CoefficientList[Series[Exp[u],{x,0,20}],x]

Formula

E.g.f.: exp(A(x)) where A(x) is the e.g.f. for A036774.

a(n) ~ sqrt(2-sqrt(2)) * (1+sqrt(2))^(n+1) * exp(sqrt(2)-n) * n^(n-1). - Vaclav Kotesovec, Sep 25 2013