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Search: id:A104525
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| A104525 |
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The number of hierarchical orderings among the parts of the integer partitions of the integer n. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
Thomas Wieder, Comments on A104525
Thomas Wieder, Home Page.
Thomas Wieder, (Old) Home Page.
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FORMULA
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A104525 is the Euler transform of A055887 = number of ordered partitions of partitions.
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EXAMPLE
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Let * denote an element, let : be separator among different levels within a hierarchy, let | be a separator between different hierarchies. Furthermore, the braces {} indicate a frame. For n=3 one has a(3) = 12 because
{*:**}, {*:*}:{*}, {*}:{**}, {*:*:*}, {*}:{*}:{*}, {**}|{*}, {*}|{*:*}, {*}|{*}|{*}, {**}:{*}, {*}:{*:*}, {*}:{*}|{*}, {***}.
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MAPLE
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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); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Feb 02 2009]
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CROSSREFS
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Cf. A109186, A055887, A034691, A104460, A034899, A104500.
Sequence in context: A009532 A056274 A058353 this_sequence A126986 A090576 A152174
Adjacent sequences: A104522 A104523 A104524 this_sequence A104526 A104527 A104528
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KEYWORD
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nonn
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AUTHOR
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Thomas Wieder (wieder.thomas(AT)t-online.de), Mar 12 2005. Definition revised Mar 28 2009
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Feb 02 2009
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