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A038063
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Prod{k=1..inf}(1/(1-x^k)^a(k)) = 1+2x.
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10
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Apart from initial terms, exponents in expansion of A065472 as a product zeta(n)^(-a(n)).
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LINKS
| G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]
N. J. A. Sloane, Euler transform
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FORMULA
| a(n) = 1/n*Sum_{d divides n} (-1)^(d+1)*mobius(n/d)*2^d. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 06 2002
G.f.: Sum_{n>=1} moebius(n)*log(1 + 2*x^n)/n, where moebius(n)=A008683(n). [From Paul D. Hanna (pauldhanna(AT)juno.com), Oct 13 2010]
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PROG
| (PARI) {a(n)=polcoeff(sum(k=1, n, moebius(k)/k*log(1+2*x^k+x*O(x^n))), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Oct 13 2010]
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CROSSREFS
| Cf. A038064-A038070, A065472.
With n>1 and n=0, 1, 3 (mod 4), a(n)=A001037(n)=A059966(n)=A060477(n).
Sequence in context: A120877 A193917 A089135 * A085204 A055375 A091533
Adjacent sequences: A038060 A038061 A038062 * A038064 A038065 A038066
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KEYWORD
| sign
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Jan 04 1999.
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