A127393 Expansion of k/q^(1/2) in powers of q, where k is the elliptic function defined by sqrt(k) = theta_2/theta_3.

4, -16, 56, -160, 404, -944, 2072, -4320, 8648, -16720, 31360, -57312, 102364, -179104, 307672, -519808, 864960, -1419456, 2299832, -3682400, 5831784, -9141808, 14194200, -21842368, 33329700, -50456352, 75813240, -113107872, 167616832, -246811504, 361218392, -525598496

Offset

0,1

Comments

The elliptic modulus k is often used in elliptic integrals. - Michael Somos, Jun 11 2017

Links

Table of n, a(n) for n=0..31.

Formula

a(n) = 4*A001938(n).

k = 4*q^(1/2) - 16*q^(3/2) + 56*q^(5/2) - 160*q^(7/2) + ... where the nome q = e^(-Pi*K'/K). - Michael Somos, Jun 11 2017

Example

G.f. = 4 - 16*x + 56*x^2 - 160*x^3 + 404*x^4 - 944*x^5 + ... - Michael Somos, Jan 26 2025

Crossrefs

See A001938, the main entry for this sequence, for further information.

Sequence in context: A333282 A212520 A115108 * A239988 A308288 A340257

Adjacent sequences: A127390 A127391 A127392 * A127394 A127395 A127396

Keyword

sign

Author

N. J. A. Sloane, Apr 01 2007

Status

approved