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A284320
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Expansion of Product_{k>=0} (1 - x^(5*k+3)) in powers of x.
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4
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1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 2, 0, -1, -1, 0, 2, 0, -1, -1, 0, 3, 0, -1, -2, 0, 3, 0, -1, -3, 0, 4, 1, -1, -4, 0, 4, 1, -1, -5, 0, 5, 2, -1, -7, 0, 5, 3, -1, -8, 0, 6, 5, -1, -10, -1, 6, 6, -1, -12, -1, 7, 9, -1, -14, -2, 7, 11
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OFFSET
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0,22
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LINKS
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FORMULA
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a(n) = -(1/n)*Sum_{k=1..n} A284281(k)*a(n-k), a(0) = 1.
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MATHEMATICA
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CoefficientList[Series[Product[1 - x^(5k + 3), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 25 2017 *) (* or *)
a[0]=1; a[n_]:=a[n]= -(1/n) Sum[ a[n-k] DivisorSum[k, # &, Mod[#, 5] == 3 &], {k, n}]; a /@ Range[0, 100] (* Giovanni Resta, Mar 25 2017 *)
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PROG
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(PARI) Vec(prod(k=0, 100, 1 - x^(5*k + 3)) + O(x^101)) \\ Indranil Ghosh, Mar 25 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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