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A104525 The number of hierarchical orderings among the parts of the integer partitions of the integer n. 2
1, 4, 12, 40, 123, 395, 1227, 3851, 11944, 37032, 114144, 351040, 1075316, 3285398, 10007731, 30409157, 92169561, 278738219, 841132013, 2533138770, 7614144053, 22845435104, 68427663680, 204623945617, 610951554377, 1821438443615, 5422608839874, 16121857331124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Euler transform of A055887 = number of ordered partitions of partitions.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..750

N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.

Thomas Wieder, Comments on A104525

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 frame. For n=3 one has a(3) = 12 because:

{*:**}, {*:*}:{*}, {*}:{**}, {*:*:*}, {*}:{*}:{*}, {**}|{*}, {*}|{*:*}, {*}|{*}|{*}, {**}:{*}, {*}:{*:*}, {*}:{*}|{*}, {***}.

MAPLE

We can use combstruct to actually construct the structures A104525(n). %1 := Sequence(Set(Set(Z))).

with(combinat): with (numtheory): b:= proc(n) local k; option remember; `if`(n=0, 1, add (numbpart(k) * b(n-k), k=1..n)) end: a:= proc(n) option remember; `if` (n=0, 1, add (add (d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n) end: seq (a(n), n=1..30); # Alois P. Heinz, Feb 02 2009

MATHEMATICA

max = 30; A055887 = CoefficientList[1/(2 - 1/QPochhammer[x, x]) + O[x]^(max + 1), x] ; s = 1/Product[(1 - x^n)^A055887[[n + 1]], {n, 1, max}] + O[x]^max; CoefficientList[s, x] // Rest (* Jean-Fran├žois Alcover, Jan 10 2016 *)

CROSSREFS

Cf. A034691, A034899, A055887, A104460, A104500, A109186.

Sequence in context: A265127 A056274 A058353 * A126986 A090576 A152174

Adjacent sequences:  A104522 A104523 A104524 * A104526 A104527 A104528

KEYWORD

nonn

AUTHOR

Thomas Wieder, Mar 12 2005. Definition revised Mar 28 2009

EXTENSIONS

More terms from Alois P. Heinz, Feb 02 2009

STATUS

approved

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Last modified November 18 13:22 EST 2018. Contains 317306 sequences. (Running on oeis4.)