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A301594
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Expansion of Product_{k>=1} (1 + x^k)^A001615(k), where A001615 is the Dedekind psi function.
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6
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1, 1, 3, 7, 13, 27, 55, 99, 185, 341, 604, 1064, 1863, 3181, 5411, 9123, 15167, 25051, 41083, 66715, 107703, 172735, 275034, 435484, 685753, 1073481, 1672160, 2592070, 3998278, 6140196, 9389302, 14296376, 21682534, 32759202, 49308812, 73956692, 110545113
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ exp(3^(5/3) * (5*Zeta(3))^(1/3) * n^(2/3) / (2^(4/3) * Pi^(2/3)) - Pi^(2/3) * n^(1/3) / (2^(5/3) * 3^(2/3) * (5*Zeta(3))^(1/3)) - Pi^2 / (2160 * Zeta(3))) * (5*Zeta(3))^(1/6) / (2^(3/4) * 3^(1/6) * Pi^(5/6) * n^(2/3)).
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[k*Sum[MoebiusMu[d]^2 / d, {d, Divisors @ k}] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 31 2018 *)
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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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