A124344 Number of ordered rooted trees on n nodes with thinning limbs.

1, 1, 2, 4, 10, 25, 68, 187, 530, 1523, 4447, 13121, 39107, 117490, 355507, 1082234, 3312255, 10185125, 31450633, 97480337, 303157086, 945671951, 2958113722, 9276528602, 29158191215, 91845796986, 289874628176, 916536727561

Offset: 1

Author

Christian G. Bower, Oct 30 2006, suggested by Franklin T. Adams-Watters

Keywords

• nonn

Comments

A rooted tree with thinning limbs is such that if a node has k children, all its children have at most k children.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A000108, A124343-A124348.

Row sums of A124328.

Formula

G.f.: A(x) = A0(x)+A1(x)+A2(x)+... where A0(x)=x, An(x) = x*(A0(x)+A1(x)+...+An(x))^n.