A307901 Expansion of 1/(1 - x * theta_4(x)), where theta_4() is the Jacobi theta function.

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

Robert Israel, Table of n, a(n) for n = 0..5045

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

Cf. A002448, A015128, A032803, A299108.

Sequence in context: A279939 A337748 A286511 * A232965 A249401 A196845

Adjacent sequences: A307898 A307899 A307900 * A307902 A307903 A307904

Keyword

sign

Author

Ilya Gutkovskiy, May 04 2019

Status

approved