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A307901
Expansion of 1/(1 - x * theta_4(x)), where theta_4() is the Jacobi theta function.
1
1, 1, -1, -3, -1, 7, 11, -5, -33, -25, 53, 123, 9, -297, -363, 323, 1273, 657, -2415, -4407, 957, 12069, 11465, -16887, -47915, -12939, 104431, 152029, -85529, -476579, -333905, 803237, 1752799, 11597, -4349949, -5019855, 5068735, 18311655, 8392559, -35953969
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
FORMULA
G.f.: Sum_{k>=0} x^k * theta_4(x)^k.
G.f.: 1/(1 - x * Sum_{k=-oo..oo} (-1)^k * x^(k^2)).
G.f.: 1/(1 - x * Product_{k>=1} (1 - x^k)/(1 + x^k)).
MAPLE
S:= series(1/(1-x*JacobiTheta4(0, x)), x, 101):
seq(coeff(S, x, j), j=0..100); # Robert Israel, Nov 03 2019
MATHEMATICA
nmax = 39; CoefficientList[Series[1/(1 - x EllipticTheta[4, 0, x]), {x, 0, nmax}], x]
nmax = 39; CoefficientList[Series[1/(1 - x Product[(1 - x^k)/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 04 2019
STATUS
approved