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A281542
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Expansion of Sum_{i>=1} x^(i^2)/(1 + x^(i^2)) * Product_{j>=1} (1 + x^(j^2)).
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5
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1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 2, 3, 0, 1, 2, 0, 0, 2, 3, 0, 0, 0, 3, 5, 0, 0, 5, 7, 0, 0, 0, 2, 3, 1, 2, 3, 4, 2, 5, 3, 0, 0, 5, 7, 0, 0, 4, 9, 4, 2, 5, 7, 5, 3, 4, 2, 3, 0, 5, 10, 4, 1, 11, 12, 0, 2, 6, 7, 4, 0, 2, 12, 12, 0, 6, 15, 9, 2, 8, 7, 3, 7, 8, 10, 9, 5, 8, 21, 13, 0, 7, 19, 13, 0, 2, 10, 13, 8
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OFFSET
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1,5
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COMMENTS
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Total number of parts in all partitions of n into distinct squares.
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LINKS
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FORMULA
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G.f.: Sum_{i>=1} x^(i^2)/(1 + x^(i^2)) * Product_{j>=1} (1 + x^(j^2)).
a(n) = Sum_{k>=0} k * A341040(n,k).
a(n) = 0 <=> n in { A001422 }. (End)
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EXAMPLE
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a(26) = 5 because we have [25, 1], [16, 9 ,1] and 2 + 3 = 5.
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MATHEMATICA
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nmax = 100; Rest[CoefficientList[Series[Sum[x^i^2/(1 + x^i^2), {i, 1, nmax}] Product[1 + x^j^2, {j, 1, nmax}], {x, 0, nmax}], x]]
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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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