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A255404 Number of different integer partitions of n that produce the maximum number of set partitions for a set of cardinality n. 1
1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 3, 2, 1, 4, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 4, 6, 4, 1, 2, 1, 5, 5, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 5, 2, 2, 1, 1, 4, 1, 1, 2, 3, 1, 8, 2, 1, 1, 3, 1, 1, 1, 3, 1, 1, 3, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 3, 2, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

If n=Sum_i[n_i], the number of set partitions can be written as sp=n!/Prod_i,j(n_i!m_j!) where m_j is the multiplicity of the integer j in the n_i's. For certain integers, this number is maximized by more than one partition.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

For n=9, {1,1,2,2,3} maximizes the number of set partitions, while for n=10, this number is maximized by {1,2,3,4}, {1,1,2,3,3}, {1,2,2,2,3} and {1,1,1,2,2,3}.

MATHEMATICA

Prod[l_] := Apply[Times, Map[#! &, l]]*

    Apply[Times, Map[Count[l, #]! &, Range[Max[Length[l]]]]]

b[n_] := (Min[Map[Prod, IntegerPartitions[n]]])

a[n_] := Count[Map[Prod, IntegerPartitions[n]], b[n]]

Table[a[n], {n, 0, 20}] (* after A102356 *)

CROSSREFS

Cf. A102356, A102456.

Sequence in context: A062378 A073753 A290602 * A078090 A174341 A168516

Adjacent sequences:  A255401 A255402 A255403 * A255405 A255406 A255407

KEYWORD

nonn

AUTHOR

Andrei Cretu, Feb 22 2015

EXTENSIONS

More terms from Alois P. Heinz, Feb 25 2015

STATUS

approved

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Last modified April 11 14:58 EDT 2021. Contains 342886 sequences. (Running on oeis4.)