OFFSET
1,2
COMMENTS
The next term is too large to include (282 digits).
First differences of A110387.
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
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jan 09 2015
STATUS
approved