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A281244
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Expansion of Product_{k>=1} (1 + x^(6*k-1)).
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12
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1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 2, 3, 1, 0, 0, 0, 3, 4, 1, 0, 0, 1, 4, 4, 1, 0, 0, 1, 5, 5, 1, 0, 0, 2, 7, 5, 1, 0, 0, 3, 8, 6, 1, 0, 0, 5, 10, 6, 1, 0, 1
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OFFSET
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0,29
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COMMENTS
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LINKS
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FORMULA
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a(n) ~ exp(sqrt(n/2)*Pi/3) / (2^(25/12)*sqrt(3)*n^(3/4)) * (1 + (Pi/144 - 9/(4*Pi)) / sqrt(2*n)).
G.f.: Sum_{k>=0} x^(k*(3*k + 2)) / Product_{j=1..k} (1 - x^(6*j)). - Ilya Gutkovskiy, Nov 24 2020
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(add(
[0$5, 1, 0$4, -1, 1][1+irem(d, 12)]*d, d=
numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
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MATHEMATICA
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nmax = 200; CoefficientList[Series[Product[(1 + x^(6*k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 200; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 6] == 5, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly
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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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