OFFSET
0,3
COMMENTS
We define the alternating product of a sequence (y_1,...,y_k) to be Product_i y_i^((-1)^(i-1)).
EXAMPLE
Partitions representing each of the a(7) = 10 alternating products are:
(7) -> 7
(61) -> 6
(52) -> 5/2
(511) -> 5
(43) -> 4/3
(421) -> 2
(4111) -> 4
(331) -> 1
(322) -> 3
(3211) -> 3/2
MATHEMATICA
altprod[q_]:=Product[q[[i]]^(-1)^(i-1), {i, Length[q]}];
Table[Length[Union[altprod/@IntegerPartitions[n]]], {n, 0, 30}]
CROSSREFS
The version for alternating sum is A004526.
The reverse version is A347462.
A000041 counts partitions.
A027187 counts partitions of even length.
A027193 counts partitions of odd length.
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.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 06 2021
STATUS
approved