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), the sum of the divisors of n.
EXAMPLE
O.g.f.: A(x) = 1 + 2*x + 10*x^2 + 44*x^3 + 134*x^4 + 468*x^5 + 1524*x^6 +...
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 +...+ A054785(n^3)*x^n/n +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, (sigma(2*m^3)-sigma(m^3))*x^m/m)+x^2*O(x^n)), n)}
for(n=0, 50, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 21 2013
STATUS
approved