OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
FORMULA
G.f.: Product_{k>=1} (theta_3(x^k)/theta_4(x^k))^tau(k), where tau = number of divisors (A000005).
G.f.: Product_{i>=1, j>=1} (Sum_{k=-oo..+oo} x^(i*j*k^2))/(Sum_{k=-oo..+oo} (-1)^k*x^(i*j*k^2)).
G.f.: Product_{i>=1, j>=1, k>=1} (1 + x^(i*j*k))^4/(1 + x^(2*i*j*k))^2.
G.f.: Product_{k>=1} (1 + x^k)^(4*tau_3(k))/(1 + x^(2*k))^(2*tau_3(k)), where tau_3 = A007425.
MATHEMATICA
nmax = 29; CoefficientList[Series[Product[Product[EllipticTheta[3, 0, x^(i j)]/EllipticTheta[4, 0, x^(i j)], {j, 1, nmax}], {i, 1, nmax}], {x, 0, nmax}], x]
nmax = 29; CoefficientList[Series[Product[(EllipticTheta[3, 0, x^k]/EllipticTheta[4, 0, x^k])^DivisorSigma[0, k], {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 18 2019
STATUS
approved