A248099 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.

1, 4, 216, 2428912656, 84539502447168140812774402430429967453919558368

Offset

1,2

Comments

The next term is too large to include (282 digits).

First differences of A110387.

Links

Table of n, a(n) for n=1..5.

Formula

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

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);

Crossrefs

Cf. A110387.

Sequence in context: A038786 A268362 A072694 * A068210 A078693 A222421

Adjacent sequences: A248096 A248097 A248098 * A248100 A248101 A248102

Keyword

nonn

Author

Emeric Deutsch, Jan 09 2015

Status

approved