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A327727
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Expansion of Product_{i>=1, j>=0} (1 + x^(i*2^j)) / (1 - x^(i*2^j)).
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0
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1, 2, 6, 12, 28, 52, 104, 184, 340, 578, 1004, 1652, 2752, 4404, 7088, 11080, 17362, 26592, 40730, 61284, 92096, 136408, 201608, 294456, 428952, 618658, 889684, 1268624, 1803520, 2545164, 3580784, 5005584, 6976046, 9667164, 13356364, 18360368, 25165732
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: Product_{k>=1} ((1 + x^k) / (1 - x^k))^A001511(k).
G.f.: Product_{k>=1} 1 / (1 - x^k)^(A001511(k) + 1).
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MATHEMATICA
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nmax = 36; CoefficientList[Series[Product[1/(1 - x^k)^(IntegerExponent[2 k, 2] + 1), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (IntegerExponent[2 d, 2] + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 36}]
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PROG
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(PARI) seq(n)={Vec(1/prod(k=1, n, (1 - x^k + O(x*x^n))^(2+valuation(k, 2))))} \\ Andrew Howroyd, Sep 23 2019
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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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