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A218570
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Number of partitions p of n such that max(p)-min(p) = 7.
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3
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1, 1, 3, 3, 7, 8, 14, 18, 28, 34, 51, 63, 86, 108, 144, 175, 229, 278, 351, 425, 529, 630, 775, 919, 1109, 1309, 1565, 1827, 2167, 2518, 2952, 3414, 3975, 4563, 5281, 6036, 6931, 7889, 9012, 10200, 11598, 13078, 14785, 16613, 18704, 20925, 23470, 26174, 29229
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OFFSET
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9,3
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LINKS
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FORMULA
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G.f.: Sum_{k>0} x^(2*k+7)/Product_{j=0..7} (1-x^(k+j)).
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MATHEMATICA
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terms = 49; offset = 9; max = terms + offset; s[k0_ /; k0 > 0] := Sum[x^(2*k + k0)/Product[ (1 - x^(k + j)), {j, 0, k0}], {k, 1, Ceiling[max/2]}] + O[x]^max // CoefficientList[#, x] &; Drop[s[7], offset] (* Jean-François Alcover, Sep 11 2017, after Alois P. Heinz *)
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CROSSREFS
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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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