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

1,2

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

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

Prog

(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

Crossrefs

Cf. A108521-A108529, A007151, A001147.

Sequence in context: A201862 A167016 A300014 * A014500 A101482 A099717

Adjacent sequences: A108519 A108520 A108521 * A108523 A108524 A108525

Keyword

nonn

Author

Christian G. Bower, Jun 07 2005

Status

approved