cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, May 04 2019

Keywords

Crossrefs

Programs

  • 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]

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)).