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A240076
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Number of partitions of n such that m(greatest part) < m(1), where m = multiplicity.
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5
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0, 0, 0, 0, 1, 2, 3, 6, 8, 13, 18, 27, 35, 52, 67, 93, 121, 164, 209, 279, 353, 461, 582, 748, 935, 1191, 1480, 1861, 2302, 2870, 3526, 4365, 5335, 6554, 7976, 9736, 11789, 14316, 17259, 20844, 25032, 30092, 35992, 43086, 51347, 61215, 72710, 86361, 102235
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OFFSET
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0,6
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LINKS
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FORMULA
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EXAMPLE
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a(7) counts these 6 partitions: 511, 4111, 3211, 31111, 22111, 211111.
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MATHEMATICA
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z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Count[p, Max[p]] < Count[p, 1]], {n, 0, z}] (* A240076 *)
t2 = Table[Count[f[n], p_ /; Count[p, Max[p]] <= Count[p, 1]], {n, 0, z}] (* A240077 *)
t3 = Table[Count[f[n], p_ /; Count[p, Max[p]] == Count[p, 1]], {n, 0, z}] (* A240078 *)
t4 = Table[Count[f[n], p_ /; Count[p, Max[p]] > Count[p, 1]], {n, 0, z}] (* A117995 *)
t5 = Table[Count[f[n], p_ /; Count[p, Max[p]] >= Count[p, 1]], {n, 0, z}] (* A240080 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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