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A321194 Regular triangle where T(n,k) is the number of non-isomorphic multiset partitions of weight n with k connected components. 8
1, 3, 1, 6, 3, 1, 17, 12, 3, 1, 40, 35, 12, 3, 1, 125, 112, 45, 12, 3, 1, 354, 347, 148, 45, 12, 3, 1, 1159, 1122, 512, 163, 45, 12, 3, 1, 3774, 3651, 1724, 572, 163, 45, 12, 3, 1, 13113, 12320, 5937, 2020, 593, 163, 45, 12, 3, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

O.g.f.: Product 1/(1 - t*x^n)^A007718(n).

EXAMPLE

Triangle begins:

      1

      3     1

      6     3     1

     17    12     3     1

     40    35    12     3     1

    125   112    45    12     3     1

    354   347   148    45    12     3     1

   1159  1122   512   163    45    12     3     1

   3774  3651  1724   572   163    45    12     3     1

  13113 12320  5937  2020   593   163    45    12     3     1

The fourth row counts the following non-isomorphic multiset partitions.

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

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

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

  {{1,2,3,3}}        {{1,2},{3,3}}

  {{1,2,3,4}}        {{1},{2,3,4}}

  {{1},{1,1,1}}      {{1,2},{3,4}}

  {{1,1},{1,1}}      {{1},{1},{2,2}}

  {{1},{1,2,2}}      {{1},{1},{2,3}}

  {{1,2},{1,2}}      {{1},{2},{2,2}}

  {{1,2},{2,2}}      {{1},{3},{2,3}}

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

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

  {{3},{1,2,3}}

  {{1},{1},{1,1}}

  {{1},{2},{1,2}}

  {{2},{2},{1,2}}

  {{1},{1},{1},{1}}

CROSSREFS

First column is A007718. Row sums are A007716.

Cf. A006126, A048143, A143543, A306005, A316983, A317672, A317674, A319616, A321155.

Sequence in context: A094504 A107884 A185628 * A158822 A226132 A121443

Adjacent sequences:  A321191 A321192 A321193 * A321195 A321196 A321197

KEYWORD

nonn,tabl

AUTHOR

Gus Wiseman, Oct 29 2018

STATUS

approved

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Last modified March 24 11:49 EDT 2019. Contains 321448 sequences. (Running on oeis4.)