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A038063
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Product_{k>=1}1/(1 - x^k)^a(k) = 1 + 2x.
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12
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2, -3, 2, -3, 6, -11, 18, -30, 56, -105, 186, -335, 630, -1179, 2182, -4080, 7710, -14588, 27594, -52377, 99858, -190743, 364722, -698870, 1342176, -2581425, 4971008, -9586395, 18512790, -35792449, 69273666, -134215680, 260300986
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OFFSET
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1,1
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COMMENTS
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Apart from initial terms, exponents in expansion of A065472 as a product zeta(n)^(-a(n)).
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LINKS
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FORMULA
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a(n) = 1/n*Sum_{d divides n} (-1)^(d+1)*mobius(n/d)*2^d. - Vladeta Jovovic, Sep 06 2002
G.f.: Sum_{n>=1} moebius(n)*log(1 + 2*x^n)/n, where moebius(n)=A008683(n). - Paul D. Hanna, Oct 13 2010
For n == 0, 1, 3 (mod 4), a(n) = (-1)^(n+1)*A001037(n), which for n>1 also equals (-1)^(n+1)*A059966(n) = (-1)^(n+1)*A060477(n).
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PROG
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(PARI) {a(n)=polcoeff(sum(k=1, n, moebius(k)/k*log(1+2*x^k+x*O(x^n))), n)} \\ Paul D. Hanna, Oct 13 2010
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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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