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A322133 Regular triangle read by rows where T(n,k) is the number of non-isomorphic connected multiset partitions of weight n with k vertices. 2
1, 0, 1, 0, 2, 1, 0, 3, 2, 1, 0, 5, 8, 3, 1, 0, 7, 17, 12, 3, 1, 0, 11, 46, 45, 18, 4, 1, 0, 15, 94, 141, 76, 23, 4, 1, 0, 22, 212, 432, 333, 124, 30, 5, 1, 0, 30, 416, 1231, 1254, 622, 178, 37, 5, 1, 0, 42, 848, 3346, 4601, 2914, 1058, 252, 45, 6, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

Triangle begins:

    1

    0    1

    0    2    1

    0    3    2    1

    0    5    8    3    1

    0    7   17   12    3    1

    0   11   46   45   18    4    1

    0   15   94  141   76   23    4    1

    0   22  212  432  333  124   30    5    1

    0   30  416 1231 1254  622  178   37    5    1

    0   42  848 3346 4601 2914 1058  252   45    6    1

Non-isomorphic representatives of the multiset partitions counted in row 4:

  {{1,1,1,1}}        {{1,1,2,2}}      {{1,2,3,3}}    {{1,2,3,4}}

  {{1},{1,1,1}}      {{1,2,2,2}}      {{1,3},{2,3}}

  {{1,1},{1,1}}      {{1},{1,2,2}}    {{3},{1,2,3}}

  {{1},{1},{1,1}}    {{1,2},{1,2}}

  {{1},{1},{1},{1}}  {{1,2},{2,2}}

                     {{2},{1,2,2}}

                     {{1},{2},{1,2}}

                     {{2},{2},{1,2}}

CROSSREFS

Row sums are A007718.

Cf. A000664, A007716, A054923, A191646, A191970, A275421, A286520, A317672, A319719, A321155, A321254, A322114.

Sequence in context: A180653 A259100 A096652 * A274183 A212278 A244215

Adjacent sequences:  A322130 A322131 A322132 * A322134 A322135 A322136

KEYWORD

nonn,tabl

AUTHOR

Gus Wiseman, Nov 27 2018

STATUS

approved

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)