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A055884 Euler transform of partition triangle A008284. 7
1, 1, 2, 1, 2, 3, 1, 4, 4, 5, 1, 4, 8, 7, 7, 1, 6, 12, 16, 12, 11, 1, 6, 17, 25, 28, 19, 15, 1, 8, 22, 43, 49, 48, 30, 22, 1, 8, 30, 58, 87, 88, 77, 45, 30, 1, 10, 36, 87, 134, 167, 151, 122, 67, 42, 1, 10, 45, 113, 207, 270, 296, 247, 185, 97, 56, 1, 12, 54, 155, 295, 448 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Number of multiset partitions of length-k integer partitions of n. - Gus Wiseman, Nov 09 2018

LINKS

Table of n, a(n) for n=1..72.

N. J. A. Sloane, Transforms

EXAMPLE

1; 1,2; 1,2,3; 1,4,4,5; 1,4,8,7,7; ...

From Gus Wiseman, Nov 09 2018: (Start)

Triangle begins:

   1

   1   2

   1   2   3

   1   4   4   5

   1   4   8   7   7

   1   6  12  16  12  11

   1   6  17  25  28  19  15

   1   8  22  43  49  48  30  22

   1   8  30  58  87  88  77  45  30

The fifth row {1, 4, 8, 7, 7} counts the following multiset partitions:

  {{5}}   {{1,4}}     {{1,1,3}}       {{1,1,1,2}}         {{1,1,1,1,1}}

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

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

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

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

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

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

                    {{1},{2},{2}}

(End)

MATHEMATICA

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];

mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];

Table[Length[Join@@mps/@IntegerPartitions[n, {k}]], {n, 5}, {k, n}] (* Gus Wiseman, Nov 09 2018 *)

CROSSREFS

Row sums give A001970. Cf. A055885, A055886.

Cf. A000219, A007716, A008284, A255906, A317449, A317532, A317533, A320796, A320801, A320808.

Sequence in context: A110582 A162507 A091298 * A055889 A125930 A210790

Adjacent sequences:  A055881 A055882 A055883 * A055885 A055886 A055887

KEYWORD

nonn,tabl

AUTHOR

Christian G. Bower, Jun 09 2000

STATUS

approved

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Last modified January 22 11:56 EST 2019. Contains 319363 sequences. (Running on oeis4.)