%I #8 May 20 2013 23:29:12

%S 1,1,-2,2,-1,-7,8,-14,1,11,-23,43,-54,38,17,-55,162,-198,257,-175,69,

%T 141,-518,764,-1049,1215,-1241,549,161,-1625,3192,-5176,6782,-7568,

%U 7267,-4263,-788,8394,-17866,29782,-39041,46101,-45857,36551,-14591,-20937,70638,-129520,190994,-245846,280560

%N G.f.: exp( Sum_{n>=1} A002129(n^2)*x^n/n ), where A002129(n) is the excess of sum of odd divisors of n over sum of even divisors of n.

%C Compare to: Sum_{n>=0} x^(n*(n+1)/2) = exp( Sum_{n>=1} A002129(n)*x^n/n ).

%H Paul D. Hanna, <a href="/A225925/b225925.txt">Table of n, a(n) for n = 0..1000</a>

%e G.f.: A(x) = 1 + x - 2*x^2 + 2*x^3 - x^4 - 7*x^5 + 8*x^6 - 14*x^7 + x^8 +...

%e where

%e log(A(x)) = x - 5*x^2/2 + 13*x^3/3 - 29*x^4/4 + 31*x^5/5 - 65*x^6/6 + 57*x^7/7 - 125*x^8/8 + 121*x^9/9 - 155*x^10/10 +...+ A002129(n^2)*x^n/n +...

%o (PARI) {A002129(n)=if(n<1, 0, -sumdiv(n, d, (-1)^d*d))}

%o {a(n)=polcoeff(exp(sum(k=1,n,A002129(k^2)*x^k/k)+x*O(x^n)),n)}

%o for(n=0,50,print1(a(n),", "))

%Y Cf. A224340, A224339, A002129; variant: A215603.

%K sign

%O 0,3

%A _Paul D. Hanna_, May 20 2013