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%I A347462 #6 Oct 27 2021 22:22:58
%S A347462 1,1,2,3,4,6,8,11,13,17,22,28,33,42,51,59,69,84,100,117,137,163,191,
%T A347462 222,256,290,332,378,429,489,564,643,729,819,929,1040,1167,1313,1473,
%U A347462 1647,1845,2045,2272,2521,2785,3076,3398,3744,4115,4548,5010,5524,6086
%N A347462 Number of distinct possible reverse-alternating products of integer partitions of n.
%C A347462 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.
%e A347462 Partitions representing each of the a(7) = 11 reverse-alternating products:
%e A347462      (7) -> 7
%e A347462     (61) -> 1/6
%e A347462     (52) -> 2/5
%e A347462    (511) -> 5
%e A347462     (43) -> 3/4
%e A347462    (421) -> 2
%e A347462   (4111) -> 1/4
%e A347462    (331) -> 1
%e A347462    (322) -> 3
%e A347462   (3211) -> 2/3
%e A347462   (2221) -> 1/2
%t A347462 revaltprod[q_]:=Product[Reverse[q][[i]]^(-1)^(i-1),{i,Length[q]}];
%t A347462 Table[Length[Union[revaltprod/@IntegerPartitions[n]]],{n,0,30}]
%Y A347462 The version for non-reverse alternating sum instead of product is A004526.
%Y A347462 Counting only integers gives A028310, non-reverse A347707.
%Y A347462 The version for factorizations is A038548, non-reverse A347460.
%Y A347462 The non-reverse version is A347461.
%Y A347462 A000041 counts partitions.
%Y A347462 A027187 counts partitions of even length.
%Y A347462 A027193 counts partitions of odd length.
%Y A347462 A103919 counts partitions by sum and alternating sum (reverse: A344612).
%Y A347462 A108917 counts knapsack partitions, ranked by A299702.
%Y A347462 A122768 counts distinct submultisets of partitions.
%Y A347462 A126796 counts complete partitions.
%Y A347462 A293627 counts knapsack factorizations by sum.
%Y A347462 A301957 counts distinct subset-products of prime indices.
%Y A347462 A304792 counts subset-sums of partitions, positive A276024, strict A284640.
%Y A347462 A304793 counts distinct positive subset-sums of prime indices.
%Y A347462 A325534 counts separable partitions, ranked by A335433.
%Y A347462 A325535 counts inseparable partitions, ranked by A335448.
%Y A347462 Cf. A000070, A001055, A002033, A002219, A028983, A119620, A325768, A345926, A347443, A347444, A347445, A347446.
%K A347462 nonn
%O A347462 0,3
%A A347462 _Gus Wiseman_, Oct 06 2021

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