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A280129
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Expansion of Product_{k>=2} (1 + x^(k^2)).
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8
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1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 3, 0, 0, 1, 1, 1, 0, 0, 1, 3, 0, 0, 2, 2, 0, 1, 2, 0, 1, 1, 2, 1
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OFFSET
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0,26
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COMMENTS
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Number of partitions of n into distinct squares > 1.
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LINKS
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FORMULA
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G.f.: Product_{k>=2} (1 + x^(k^2)).
a(n) = Sum_{k=0..n} (-1)^(n-k) * A033461(k).
(End)
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EXAMPLE
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G.f. = 1 + x^4 + x^9 + x^13 + x^16 + x^20 + 2*x^25 + 2*x^29 + x^34 + x^36 + ...
a(25) = 2 because we have [25] and [16, 9].
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MATHEMATICA
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nmax = 115; CoefficientList[Series[Product[1 + x^k^2, {k, 2, nmax}], {x, 0, nmax}], x]
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PROG
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(PARI) {a(n) = if(n < 0, 0, polcoeff( prod(k=2, sqrtint(n), 1 + x^k^2 + x*O(x^n)), n))}; /* Michael Somos, Dec 26 2016 */
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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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