Number of ordered trees with root degree n and having strictly thinning limbs. An ordered tree with strictly thinning limbs is such that if a node has k children, each of its children has less than k children.

a(1)=1; a(n) = (a(n-1)^{1/(n-1)} + a(n-1))^n for n>=2.

For the g.f. F[n](z) of the ordered trees with root degree n and having strictly thinning limbs, where z marks number of vertices, we have F[1](z) = z^2 and F[n] = z*(F[n-1] + (F[n-1]/z)^{1/(n-1)})^n for n>=2.

EXAMPLE

a(2)=4; indeed, we have /\ and the 3 trees obtained by hanging | to either of the leaves of /\ or to both of them.

MAPLE

a[1] := 1: for n from 2 to 6 do a[n] := simplify((a[n-1]^(1/(n-1))+a[n-1])^n) end do: seq(a[n], n = 1 .. 6);