A225925 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.

1, 1, -2, 2, -1, -7, 8, -14, 1, 11, -23, 43, -54, 38, 17, -55, 162, -198, 257, -175, 69, 141, -518, 764, -1049, 1215, -1241, 549, 161, -1625, 3192, -5176, 6782, -7568, 7267, -4263, -788, 8394, -17866, 29782, -39041, 46101, -45857, 36551, -14591, -20937, 70638, -129520, 190994, -245846, 280560

Offset: 0

Author

Paul D. Hanna, May 20 2013

Keywords

• sign

Comments

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

Examples

			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 +...
where
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 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..1000

Crossrefs

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

Programs

PARI

{A002129(n)=if(n<1, 0, -sumdiv(n, d, (-1)^d*d))}
{a(n)=polcoeff(exp(sum(k=1,n,A002129(k^2)*x^k/k)+x*O(x^n)),n)}
for(n=0,50,print1(a(n),", "))