Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Jan 10 2015 13:27:33
%S 1,4,216,2428912656,84539502447168140812774402430429967453919558368
%N 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.
%C The next term is too large to include (282 digits).
%C First differences of A110387.
%F a(1)=1; a(n) = (1 + a(1) + ... + a(n-1))^n for n>=2.
%F a(1)=1; a(n) = (a(n-1)^{1/(n-1)} + a(n-1))^n for n>=2.
%F 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.
%e a(2)=4; indeed, we have /\ and the 3 trees obtained by hanging | to either of the leaves of /\ or to both of them.
%p 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);
%Y Cf. A110387.
%K nonn
%O 1,2
%A _Emeric Deutsch_, Jan 09 2015