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%I #31 Jun 12 2018 08:18:06
%S 2,-3,2,-3,6,-11,18,-30,56,-105,186,-335,630,-1179,2182,-4080,7710,
%T -14588,27594,-52377,99858,-190743,364722,-698870,1342176,-2581425,
%U 4971008,-9586395,18512790,-35792449,69273666,-134215680,260300986
%N Product_{k>=1}1/(1 - x^k)^a(k) = 1 + 2x.
%C Apart from initial terms, exponents in expansion of A065472 as a product zeta(n)^(-a(n)).
%H Seiichi Manyama, <a href="/A038063/b038063.txt">Table of n, a(n) for n = 1..3000</a>
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a> [Cached copy]
%H N. J. A. Sloane, <a href="/transforms.txt">Euler transform</a>
%F a(n) = 1/n*Sum_{d divides n} (-1)^(d+1)*mobius(n/d)*2^d. - _Vladeta Jovovic_, Sep 06 2002
%F G.f.: Sum_{n>=1} moebius(n)*log(1 + 2*x^n)/n, where moebius(n)=A008683(n). - _Paul D. Hanna_, Oct 13 2010
%F 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).
%F For n == 2 (mod 4), a(n) = -(A001037(n) + A001037(n/2)). - _George Beck_ and _Max Alekseyev_, May 23 2016
%F a(n) ~ -(-1)^n * 2^n / n. - _Vaclav Kotesovec_, Jun 12 2018
%o (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
%Y Cf. A038064, A038065, A038066, A038067, A038068, A038069, A038070, A065472.
%K sign
%O 1,1
%A _Christian G. Bower_, Jan 04 1999
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