A318567 - OEIS

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.

1, 3, 8, 21, 54, 137, 343, 847, 2075, 5031, 12109, 28921, 68633, 161865, 379655

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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}