OFFSET
0,2
COMMENTS
Compare to the Jacobi theta_3 function:
1 + 2*Sum_{n>=1} x^(n^2) = exp( Sum_{n>=1} -(sigma(2*n) - sigma(n))*(-x)^n/n ).
Here sigma(n) = A000203(n) is the sum of divisors of n.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..1000
EXAMPLE
O.g.f.: A(x) = 1 + 2*x - 2*x^2 + 2*x^3 + 10*x^4 - 10*x^5 + 6*x^6 + 10*x^7 +...
where
log(A(x)) = 2*x - 8*x^2/2 + 26*x^3/3 - 32*x^4/4 + 62*x^5/5 - 104*x^6/6 + 114*x^7/7 - 128*x^8/8 + 242*x^9/9 - 248*x^10/10 + 266*x^11/11 - 416*x^12/12 +...+ -A054785(n^2)*(-x)^n/n +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, -(sigma(2*m^2)-sigma(m^2))*(-x)^m/m)+x^2*O(x^n)), n)}
for(n=0, 50, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Aug 17 2012
STATUS
approved