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A347462
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Number of distinct possible reverse-alternating products of integer partitions of n.
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17
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1, 1, 2, 3, 4, 6, 8, 11, 13, 17, 22, 28, 33, 42, 51, 59, 69, 84, 100, 117, 137, 163, 191, 222, 256, 290, 332, 378, 429, 489, 564, 643, 729, 819, 929, 1040, 1167, 1313, 1473, 1647, 1845, 2045, 2272, 2521, 2785, 3076, 3398, 3744, 4115, 4548, 5010, 5524, 6086
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OFFSET
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0,3
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COMMENTS
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We define the alternating product of a sequence (y_1,...,y_k) to be Product_i y_i^((-1)^(i-1)). The reverse-alternating product is the alternating product of the reversed sequence.
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LINKS
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EXAMPLE
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Partitions representing each of the a(7) = 11 reverse-alternating products:
(7) -> 7
(61) -> 1/6
(52) -> 2/5
(511) -> 5
(43) -> 3/4
(421) -> 2
(4111) -> 1/4
(331) -> 1
(322) -> 3
(3211) -> 2/3
(2221) -> 1/2
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MATHEMATICA
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revaltprod[q_]:=Product[Reverse[q][[i]]^(-1)^(i-1), {i, Length[q]}];
Table[Length[Union[revaltprod/@IntegerPartitions[n]]], {n, 0, 30}]
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CROSSREFS
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The version for non-reverse alternating sum instead of product is A004526.
The non-reverse version is A347461.
A027187 counts partitions of even length.
A027193 counts partitions of odd length.
A103919 counts partitions by sum and alternating sum (reverse: A344612).
A122768 counts distinct submultisets of partitions.
A126796 counts complete partitions.
A293627 counts knapsack factorizations by sum.
A301957 counts distinct subset-products of prime indices.
A304793 counts distinct positive subset-sums of prime indices.
Cf. A000070, A001055, A002033, A002219, A028983, A119620, A325768, A345926, A347443, A347444, A347445, A347446.
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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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