A108523 Number of rooted identity trees with n generators.

1, 1, 2, 4, 10, 27, 77, 226, 685, 2112, 6618, 20996, 67337, 217884, 710571, 2332958, 7705429, 25584035, 85346018, 285908169, 961440343, 3244259406, 10981797187, 37280278698, 126890974820, 432950169885, 1480542159038, 5073504809660

Offset: 1

Author

Christian G. Bower, Jun 07 2005

Keywords

• nonn

Comments

A generator is a leaf or a node with just one child.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• N. J. A. Sloane, Transforms
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A108521-A108529, A004111.

Programs

PARI

WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v,n,(-1)^(n-1)/n))))-1,-#v)}
seq(n)={my(v=[1]); for(n=2, n, v=concat(v, v[#v] + WeighT(concat(v,[0]))[n])); v}  \\ Andrew Howroyd, Aug 31 2018

Formula

G.f. satisfies (2-x)*A(x) = x - 1 + WEIGH(A(x)).