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A330453 Number of strict multiset partitions of multiset partitions of integer partitions of n. 0
1, 1, 3, 9, 23, 62, 161, 410, 1031, 2579, 6359, 15575, 37830, 91241, 218581, 520544, 1232431, 2902644, 6802178, 15866054, 36844016, 85202436, 196251933, 450341874, 1029709478, 2346409350, 5329371142, 12066816905, 27240224766, 61317231288, 137643961196 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of sets of nonempty multisets of nonempty multisets of positive integers with total sum n.

LINKS

Table of n, a(n) for n=0..30.

FORMULA

Weigh transform of A001970. The weigh transform of a sequence (s_1, s_2, ...) is the sequence with generating function Product_{i > 0} (1 + x^i)^s_i.

EXAMPLE

The a(4) = 23 partitions:

  ((4))  ((22))    ((31))      ((211))        ((1111))

         ((2)(2))  ((1)(3))    ((1)(21))      ((1)(111))

                   ((1))((3))  ((2)(11))      ((11)(11))

                               ((1)(1)(2))    ((1))((111))

                               ((1))((21))    ((1)(1)(11))

                               ((2))((11))    ((1))((1)(11))

                               ((1))((1)(2))  ((1)(1)(1)(1))

                               ((2))((1)(1))  ((11))((1)(1))

                                              ((1))((1)(1)(1))

MATHEMATICA

ppl[n_, k_]:=Switch[k, 0, {n}, 1, IntegerPartitions[n], _, Join@@Table[Union[Sort/@Tuples[ppl[#, k-1]&/@ptn]], {ptn, IntegerPartitions[n]}]];

Table[Length[Select[ppl[n, 3], UnsameQ@@#&]], {n, 0, 10}]

CROSSREFS

The not necessarily strict case is A007713.

Cf. A001055, A001970, A050336, A050343, A089259, A261049, A271619, A316980, A318566, A323787-A323795, A330452-A330459, A330461, A330463.

Sequence in context: A061647 A207008 A077996 * A029852 A282732 A047085

Adjacent sequences:  A330450 A330451 A330452 * A330454 A330455 A330456

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 17 2019

STATUS

approved

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Last modified September 27 09:09 EDT 2020. Contains 337380 sequences. (Running on oeis4.)