Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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