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A330456
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Number of multisets of nonempty sets of nonempty sets of positive integers with total sum n.
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1
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1, 1, 2, 5, 10, 20, 43, 84, 168, 332, 650, 1255, 2428, 4636, 8827, 16702, 31457, 58919, 109977, 204286, 378135, 697240, 1281315, 2346612, 4284654, 7799248, 14157079, 25626996, 46269838, 83330373, 149717844, 268371413, 479996794, 856661792, 1525761119, 2712050472
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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 A050342. 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) = 10 partitions:
((4)) ((13)) ((1)(12)) ((2))((2)) ((1))((1))((1))((1))
((1)(3)) ((1))((12))
((1))((3)) ((1))((1)(2))
((1))((1))((2))
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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[And@@UnsameQ@@@#, And@@UnsameQ@@@Join@@#]&]], {n, 0, 10}]
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CROSSREFS
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Cf. A001055, A001970, A007713, A050342, A050343, A063834, A089259, A270995, A279785, A330461, 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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