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A353504
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Number of integer partitions of n whose product is less than the product of their multiplicities.
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2
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0, 0, 1, 1, 1, 2, 2, 4, 4, 6, 6, 8, 9, 11, 12, 14, 14, 18, 21, 23, 26, 29, 29, 33, 36, 39, 40, 43, 44, 50, 53, 55, 59, 65, 69, 72, 78, 79, 81, 85, 92, 95, 97, 100, 103, 108, 109, 112, 118, 124, 129, 137, 139, 142, 149, 155, 159, 165, 166, 173, 178, 181, 187
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OFFSET
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0,6
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LINKS
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EXAMPLE
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The a(2) = 1 through a(9) = 6 partitions:
11 111 1111 2111 21111 22111 221111 222111
11111 111111 31111 311111 411111
211111 2111111 2211111
1111111 11111111 3111111
21111111
111111111
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Times@@#<Times@@Length/@Split[#]&]], {n, 0, 30}]
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CROSSREFS
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RHS (product of multiplicities) is counted by A266477, ranked by A005361.
The version for greater instead of less is A353505.
A353398 counts partitions with the same product of multiplicities as of shadows, ranked by A353399.
Cf. A002033, A008284, A085629, A097318, A098859, A114640, A116608, A118914, A124010, A304678, A353394, A353500, A353507.
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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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