OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..800
N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
FORMULA
Euler transform of 1, 3, 7, 18, 42, 104, 244, 585, 1373, ... = A034691.
EXAMPLE
Let * denote an element, let : denote separator among different levels within a hierarchy, let | denote a separator between different hierarchies. Furthermore, the braces {} indicate a group. For n=3 one has a(3) = 11 because
{***}, {*|*|*}, {*}{*}{*}, {*:*:*}, {*:**}, {*|**}, {*:*|*}, {*:*}{*}, {*|*}{*}, {**:*}, {*}{**}.
MAPLE
etr:= proc(p) local b; b:=proc(n) option remember; `if`(n=0, 1, add(add(d*p(d), d=numtheory[divisors](j)) *b(n-j), j=1..n)/n) end end: b:= etr(n-> 2^(n-1)): a:= etr(b): seq(a(n), n=1..30); # Alois P. Heinz, Apr 21 2012
MATHEMATICA
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[ j]}]*b[n-j], {j, 1, n}]/n]; b]; b = etr[Function[{n}, 2^(n-1)]]; a = etr[b]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Mar 05 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Wieder, Mar 11 2005
EXTENSIONS
More terms from Alois P. Heinz, Apr 21 2012
STATUS
approved