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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 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.)