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A330454
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Number of sets of nonempty sets of nonempty multisets of positive integers with total sum n.
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0
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1, 1, 2, 7, 15, 39, 94, 224, 526, 1236, 2857, 6568, 15003, 34030, 76757, 172216, 384386, 853960, 1888891, 4160524, 9128355, 19953661, 43463021, 94354292, 204182435, 440505489, 947590424, 2032730905, 4348897216, 9280361316, 19755155955, 41953293592, 88891338202
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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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Weigh transform of A261049. The weigh transform of a sequence (s_1, s_2, ...) is the sequence with generating function Product_{i > 0} (1 + x^i)^s_i.
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EXAMPLE
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The a(4) = 15 partitions:
((4)) ((22)) ((13)) ((112)) ((1111))
((1)(3)) ((1)(12)) ((1)(111))
((1))((3)) ((2)(11)) ((1))((111))
((1))((12)) ((1))((1)(11))
((2))((11))
((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[UnsameQ@@#, And@@UnsameQ@@@#]&]], {n, 0, 10}]
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CROSSREFS
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Cf. A001970, A007713, A050336, A050342, A050343, A261049, A271619, A279785, A330461, A330463, 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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