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A330458
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Number of multisets of nonempty sets of nonempty multisets of positive integers with total sum n.
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0
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1, 1, 3, 8, 20, 49, 123, 292, 701, 1653, 3874, 8977, 20711, 47344, 107692, 243382, 547264, 1224048, 2725483, 6040796, 13334354, 29316445, 64215841, 140159357, 304890958, 661097630, 1429083295, 3080159882, 6620188725, 14190463947, 30338920339, 64702805452
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OFFSET
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0,3
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LINKS
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FORMULA
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Euler transform of A261049. The Euler transform of a sequence (s_1, s_2, ...) is the sequence with generating function Product_{i > 0} 1/(1 - x^i)^s_i.
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EXAMPLE
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The a(4) = 20 partitions:
((4)) ((22)) ((13)) ((112)) ((1111))
((2))((2)) ((1)(3)) ((1)(12)) ((1)(111))
((1))((3)) ((2)(11)) ((1))((111))
((1))((12)) ((11))((11))
((2))((11)) ((1))((1)(11))
((1))((1)(2)) ((1))((1))((11))
((1))((1))((2)) ((1))((1))((1))((1))
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MATHEMATICA
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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], And@@UnsameQ@@@#&]], {n, 0, 10}]
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CROSSREFS
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Cf. A001970, A007713, A050342, A050343, A063834, A089259, A261049, A270995, A271619, A323787-A323795, A330452-A330459.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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