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A158952
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Inverse Euler transform of the number of partitions in expanding space (A023881).
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1
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1, 2, 9, 67, 625, 7903, 117649, 2105342, 43048905, 1000976352, 25937424601, 743191207969, 23298085122481, 793763217701693, 29192928060852217, 1152939097060278256, 48661191875666868481, 2185919903971766191000
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (1/n)*Sum_{d|n} sigma(d,d)*moebius(n/d).
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EXAMPLE
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Let G(x) = Sum_{n>=0} A023881(n)*x^n then
G(x) = 1 + x + 3*x^2 + 12*x^3 + 82*x^4 + 725*x^5 + 8811*x^6 +...
G(x) = 1/[(1-x)*(1-x^2)^2*(1-x^3)^9*(1-x^4)^67*(1-x^5)^625*...].
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MATHEMATICA
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Table[Sum[DivisorSigma[d, d]*MoebiusMu[n/d], {d, Divisors[n]}]/n, {n, 1, 20}] (* Vaclav Kotesovec, Oct 09 2019 *)
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PROG
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(PARI) {a(n)=(1/n)*sumdiv(n, d, sigma(d, d)*moebius(n/d))}
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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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