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A317449 Regular triangle where T(n,k) is the number of multiset partitions of strongly normal multisets of size n into k blocks, where a multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities. 4
1, 2, 2, 3, 6, 3, 5, 21, 16, 5, 7, 52, 72, 32, 7, 11, 141, 306, 216, 65, 11, 15, 327, 1113, 1160, 512, 113, 15, 22, 791, 4033, 6052, 3737, 1154, 199, 22, 30, 1780, 13586, 28749, 24325, 10059, 2317, 323, 30 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..45.

EXAMPLE

The T(3,2) = 6 multiset partitions are {{1},{1,1}}, {{1},{1,2}}, {{2},{1,1}}, {{1},{2,3}}, {{2},{1,3}}, {{3},{1,2}}.

Triangle begins:

    1

    2    2

    3    6    3

    5   21   16    5

    7   52   72   32    7

   11  141  306  216   65   11

   15  327 1113 1160  512  113   15

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]]]];

strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n];

Table[Length[Select[Join@@mps/@strnorm[n], Length[#]==k&]], {n, 6}, {k, n}]

CROSSREFS

Row sums are A035310. First and last columns are both A000041.

Cf. A001055, A007716, A045778, A255906, A281116, A317584, A317654, A317755, A317775, A317776.

Sequence in context: A196967 A210859 A209420 * A222310 A294033 A254827

Adjacent sequences:  A317446 A317447 A317448 * A317450 A317451 A317452

KEYWORD

nonn,tabl,more

AUTHOR

Gus Wiseman, Aug 06 2018

STATUS

approved

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Last modified October 14 06:55 EDT 2019. Contains 327995 sequences. (Running on oeis4.)