

A110387


a(1) = 1, a(2) = a(1) + 1, a(3) = a(2)^2 + a(1) + 1; a(n+1) = a(n)^n + a(n1)^(n1) + ... + a(2)^2 + a(1) + 1.


2




OFFSET

1,2


COMMENTS

The next term is too large to include.
a(n) = the number of ordered trees with root degree at most n1 and having strictly thinning limbs. An ordered tree with strictly thinning limbs is such that if a vertex has k children, each of its children has fewer than k children. For example, we have a(1) = 1 (the 1vertex tree) and a(2)=1 (the 1vertex tree and the 1edge tree). From here one obtains easily (i) the recurrence relation for a(n+1) given in NAME (the terms in the righthand side count successively the trees with root degrees n1, n2, ..., 1, 0, respectively) and also (ii) the recurrence relation for a(n) given in FORMULA (the first term in the righthand side counts the trees with root degree at most n2 and the second term counts the trees with root degree n1). Moreover, it follows that the terms of this sequence are the partial sums of the sequence obtained from A248099 by extending it with A248099(0) = 1.  Emeric Deutsch, Aug 11 2015


LINKS

Table of n, a(n) for n=1..6.


FORMULA

a(n) = a(n1) + (a(n1))^(n1); a(1) = 1. The 2nd Maple program is based on this.  Emeric Deutsch, Jan 08 2015


EXAMPLE

a(3) = 2^2 + 1 + 1 = 6.
a(4) = 6^3 + 2^2 + 1^1 + 1 = 222.


MAPLE

a[1]:=1: for n from 1 to 6 do a[n+1]:=1+sum(a[j]^j, j=1..n) od: seq(a[n], n=1..7); # Emeric Deutsch, Jul 31 2005
a[1]:=1: for n from 2 to 7 do a[n]:=a[n1]+a[n1]^(n1) end do: seq(a[n], n = 1 .. 7); # Emeric Deutsch, Jan 08 2015


MATHEMATICA

A110387 = {}; s = 1; Do[s += s^n; AppendTo[A110387, s], {n, 3!}]; A110387 (* Vladimir Joseph Stephan Orlovsky, Oct 10 2008 *)


PROG

(MAGMA) [n eq 1 select 1 else Self(n1)+Self(n1)^(n1): n in [1..7]]; // Vincenzo Librandi, Aug 12 2015


CROSSREFS

Cf. A248099.
Sequence in context: A285101 A176782 A013083 * A158682 A201626 A100359
Adjacent sequences: A110384 A110385 A110386 * A110388 A110389 A110390


KEYWORD

easy,nonn


AUTHOR

Amarnath Murthy, Jul 26 2005


EXTENSIONS

Corrected and extended by Emeric Deutsch and Erich Friedman, Jul 31 2005


STATUS

approved



