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.
FORMULA
Logarithmic derivative yields A227733.
EXAMPLE
G.f.: A(x) = 1 + 8*x + 52*x^2 + 288*x^3 + 1396*x^4 + 6208*x^5 + 25744*x^6 +...
where
log(A(x)) = 8*x + 40*x^2/2 + 128*x^3/3 + 176*x^4/4 + 288*x^5/5 + 640*x^6/6 +...+ A227733(n)*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, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 24 2013
STATUS
approved