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A108523
Number of rooted identity trees with n generators.
3
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
1,3
COMMENTS
A generator is a leaf or a node with just one child.
FORMULA
G.f. satisfies (2-x)*A(x) = x - 1 + WEIGH(A(x)).
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jun 07 2005
STATUS
approved