A339265 Expansion of Product_{n >= 1} (1 - x^(2*n))*(1 - x^(2*n-1))*(1 - x^(2*n+1)).

1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1

Offset

0

Comments

The sequence consists of a 1, followed by three negative ones, followed by five ones, followed by seven negative ones, and so on.

Links

Table of n, a(n) for n=0..81.

Formula

O.g.f.: A(x) = theta_4(x)/(1 - x) = 1/(1 - x) * Sum_{n >= 0 } (-1)^n*x^(n^2), where theta_4(x) is the Jacobi theta function - see A002448. Note 1/A(x) is the generating function for A211971.

Maple

series( (1 + 2*add((-1)^n*x^(n^2), n = 1..10))/(1 - x), x, 101);

Crossrefs

Cf. A002448, A211971, A255175 (partial sums), A329116 (partial sums).

Sequence in context: A097807 A014077 A174351 * A181432 A165326 A143621

Adjacent sequences: A339262 A339263 A339264 * A339266 A339267 A339268

Keyword

sign,easy

Author

Peter Bala, Nov 29 2020

Status

approved