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A318567 Number of pairs (c, y) where c is an integer composition and y is an integer partition and y can be obtained from c by choosing a partition of each part, flattening, and sorting. 3
1, 3, 8, 21, 54, 137, 343, 847, 2075, 5031, 12109, 28921, 68633, 161865, 379655 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also the number of combinatory separations of normal multisets of weight n with constant parts. A multiset is normal if it spans an initial interval of positive integers. The type of a multiset is the unique normal multiset that has the same sequence of multiplicities when its entries are taken in increasing order. For example the type of 335556 is 112223. A pair h<={g_1,...,g_k} is a combinatory separation iff there exists a multiset partition of h whose multiset of block-types is {g_1,...,g_k}.

LINKS

Table of n, a(n) for n=1..15.

EXAMPLE

The a(3) = 8 combinatory separations:

  111<={111}

  111<={1,11}

  111<={1,1,1}

  112<={1,11}

  112<={1,1,1}

  122<={1,11}

  122<={1,1,1}

  123<={1,1,1}

MATHEMATICA

Table[Sum[Length[Union[Sort/@Join@@@Tuples[IntegerPartitions/@c]]], {c, Join@@Permutations/@IntegerPartitions[n]}], {n, 30}]

CROSSREFS

Cf. A000041, A007716, A011782, A034691, A255906, A265947, A269134.

Cf. A317533, A317791, A318396, A318559, A318560, A318562, A318565.

Sequence in context: A038200 A291039 A030015 * A103446 A218482 A094723

Adjacent sequences:  A318564 A318565 A318566 * A318568 A318569 A318570

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 29 2018

STATUS

approved

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Last modified November 14 04:47 EST 2019. Contains 329108 sequences. (Running on oeis4.)