|
|
COMMENTS
| a(n) gives the number of partitions P(V(n)) of V(n)=[1,2,3,...,n]. A partition P(V(n)) acts on the components of V(n), i.e. the components of V(n) are partitioned. Therefore a(n) results as the product of the number of partitions P(i) of the component v(i)=i with i=1,...,n. For example, a(3) = 6 because we have 6 list partitions for the list V(n=3)=[1,2,3]: [[1], [1, 1], [2, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [3]], [[1], [2], [2, 1]], [[1], [2], [1, 1, 1]], [[1], [2], [3]]. - Thomas Wieder (thomas.wieder(AT)t-online.de), Sep 29 2007
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 27 2010: (Start)
Equals the eigensequence of triangle A174712; i.e. Triangle A174712 * A058694
preceded by a 1 shifts left. (End)
|
|
|
MATHEMATICA
| Table[Product[PartitionsP[k], {k, 1, n}], {n, 1, 33}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 13 2008]
|
