A108522 Number of increasing rooted trees with n generators.

1, 2, 9, 70, 771, 10948, 190205, 3907494, 92654059, 2490459468, 74827519077, 2485153213814, 90403692195179, 3574835773247140, 152675377606343901, 7003761877546096278, 343454890456254782203, 17929588055863943650988

Offset: 1

Author

Christian G. Bower, Jun 07 2005

Keywords

• nonn

Comments

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

In an increasing rooted tree, nodes are numbered and numbers increase as you move away from root.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..250
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A108521-A108529, A007151, A001147.

Programs

PARI

{a(n)=local(A=x);for(i=1,n,A=intformal((1+A)/(2-exp(A+x*O(x^n)))) );n!*polcoeff(A,n)}
for(n=1,20,print1(a(n),", ")) \\ Paul D. Hanna, Mar 29 2014

Formula

E.g.f. satisfies: 2*A(x) = x - 1 + exp(A(x)) + Integral A(x) dx. - corrected by Vaclav Kotesovec and Paul D. Hanna, Mar 29 2014

From Paul D. Hanna, Mar 29 2014: (Start)

E.g.f. satisfies: A(x) = A'(x)*(2 - exp(A(x))) - 1.

E.g.f. satisfies: A'(x) = (1 + A(x))/(2 - exp(A(x))).

(End)

a(n) ~ c * n^(n-1) / (exp(n) * r^n), where r = 0.3160173586544089316502903103262192204293322854083... and c = 0.51723490785798357350192800634304... - Vaclav Kotesovec, Mar 29 2014