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A339086
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Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 5.
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3
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1, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 0, 1, 4, 6, 0, 0, 1, 4, 6, 0, 0, 1, 6, 12, 0, 0, 1, 6, 18, 24, 0, 1, 8, 24, 24, 0, 1, 8, 30, 48, 0, 1, 10, 42, 72, 0, 1, 10, 48, 120, 120, 1, 12, 60, 144, 120, 1, 12, 72, 216, 240, 1, 14, 84, 264, 360, 1, 14, 96, 360, 600, 1, 16, 114
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OFFSET
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0,8
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} k! * x^(k*(5*k - 3)/2) / Product_{j=1..k} (1 - x^(5*j)).
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EXAMPLE
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a(18) = 6 because we have [11, 6, 1], [11, 1, 6], [6, 11, 1], [6, 1, 11], [1, 11, 6] and [1, 6, 11].
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MATHEMATICA
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nmax = 78; CoefficientList[Series[Sum[k! x^(k (5 k - 3)/2)/Product[1 - x^(5 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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Cf. A003520, A016861, A032020, A032021, A109697, A280454, A337547, A337548, A339059, A339060, A339087, A339088, A339089.
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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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