OFFSET
0,2
COMMENTS
Compare g.f. to the formula for Jacobi theta_4(x) given by:
_ theta_4(x) = exp( Sum_{n>=1} -(sigma(2*n)-sigma(n))*x^n/n )
where theta_4(x) = 1 + Sum_{n>=1} 2*(-x)^(n^2).
Here sigma(n) = A000203(n) is the sum of divisors of n.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..5000
FORMULA
EXAMPLE
G.f.: A(x) = 1 + 2*x + 6*x^2 + 18*x^3 + 42*x^4 + 102*x^5 + 238*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 +...+ A195585(n)*x^n/n +...
MATHEMATICA
nmax = 40; CoefficientList[Series[Exp[Sum[(DivisorSigma[1, 2*n^2] - DivisorSigma[1, n^2])*(x^n/n), {n, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 28 2015 *)
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, (sigma(2*m^2)-sigma(m^2))*x^m/m)+x*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 20 2011
STATUS
approved