The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A004403 Expansion of 1/theta_3(q)^2 in powers of q. 3
 1, -4, 12, -32, 76, -168, 352, -704, 1356, -2532, 4600, -8160, 14176, -24168, 40512, -66880, 108876, -174984, 277932, -436640, 679032, -1046016, 1597088, -2418240, 3632992, -5417708, 8022840, -11802176, 17252928, -25070568, 36223424, -52053760, 74414412 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Euler transform of period 4 sequence [ -4,6,-4,2,...]. REFERENCES A. Cayley, A memoir on the transformation of elliptic functions, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 9, p. 128. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 A. Cayley, A memoir on the transformation of elliptic functions, Philosophical Transactions of the Royal Society of London (1874): 397-456; Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, included in Vol. 9. [Annotated scan of pages 126-129] FORMULA Expansion of (Sum x^(n^2), n = -inf .. inf )^(-2). Expansion of elliptic function pi / 2K in powers of q. G.f.: 1 / (Sum_{k} x^k^2)^2 = (Product_{k>0} (1 + x^(2k))^2 /((1-x^k)(1 + x^k)^3))^2. a(n) = (-1)^n * A001934(n). MATHEMATICA CoefficientList[Series[1/EllipticTheta[3, 0, q]^2, {q, 0, 32}], q] (* Jean-François Alcover, Jul 18 2011 *) QP = QPochhammer; s = QP[q^2]^2/QP[-q]^4 + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 30 2015, adapted from PARI *) PROG (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 / eta(-x + A)^4, n))} /* Michael Somos, Feb 09 2006 */ (Julia) # JacobiTheta3 is defined in A000122. A004403List(len) = JacobiTheta3(len, -2) A004403List(33) |> println # Peter Luschny, Mar 12 2018 CROSSREFS Cf. A001934, A015128. Sequence in context: A361099 A138517 A001934 * A084566 A208903 A079769 Adjacent sequences: A004400 A004401 A004402 * A004404 A004405 A004406 KEYWORD sign,easy AUTHOR N. J. A. Sloane STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 7 08:38 EDT 2024. Contains 375008 sequences. (Running on oeis4.)