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A321254 Regular triangle where T(n,k) is the number of non-isomorphic connected multiset partitions of weight n with multiset density -1 <= k <= n-2. 8
1, 3, 0, 6, 0, 0, 16, 1, 0, 0, 37, 3, 0, 0, 0, 105, 18, 2, 0, 0, 0, 279, 68, 7, 0, 0, 0, 0, 817, 293, 46, 3, 0, 0, 0, 0, 2387, 1141, 228, 17, 1, 0, 0, 0, 0, 7269, 4511, 1189, 135, 9, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

Triangle begins:

     1

     3    0

     6    0    0

    16    1    0    0

    37    3    0    0    0

   105   18    2    0    0    0

   279   68    7    0    0    0    0

   817  293   46    3    0    0    0    0

  2387 1141  228   17    1    0    0    0    0

  7269 4511 1189  135    9    0    0    0    0    0

CROSSREFS

First column is A321229. Row sums are A007718.

Cf. A007716, A317672, A321155, A321194, A321253, A321255, A321256.

Sequence in context: A099892 A060147 A268142 * A262605 A092731 A201567

Adjacent sequences:  A321251 A321252 A321253 * A321255 A321256 A321257

KEYWORD

nonn,tabl

AUTHOR

Gus Wiseman, Nov 01 2018

STATUS

approved

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Last modified July 9 22:46 EDT 2020. Contains 335570 sequences. (Running on oeis4.)