The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A103640 Expansion of theta_4(q)^4 - theta_2(q)^4, where theta_2 and theta_4 are the Jacobi theta series. 2
 1, -24, 24, -96, 24, -144, 96, -192, 24, -312, 144, -288, 96, -336, 192, -576, 24, -432, 312, -480, 144, -768, 288, -576, 96, -744, 336, -960, 192, -720, 576, -768, 24, -1152, 432, -1152, 312, -912, 480, -1344, 144, -1008, 768, -1056, 288, -1872 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Eisenstein Series Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA G.f.: theta_4(q)^4 - theta_2(q)^4. - Michael Somos, May 29 2005 a(n) = (-1)^n * A004011(n). - Michael Somos, Jun 01 2012 Expansion of phi(-q)^4 - 16*q*psi(q^2)^4 in powers of q where phi(), psi() are Ramanujan theta functions. - Michael Somos, Aug 21 2014 EXAMPLE G.f. = 1 - 24*q + 24*q^2 - 96*q^3 + 24*q^4 - 144*q^5 + 96*q^6 - 192*q^7 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q]^4 - EllipticTheta[ 2, 0, q]^4, {q, 0, n}]; (* Michael Somos, Jun 01 2012 *) a[ n_] := With[{m = InverseEllipticNomeQ @x}, SeriesCoefficient[(1 - 2 m) (EllipticK[m] / (Pi/2))^2, {x, 0, n}]]; (* Michael Somos, Aug 21 2014 *) a[ n_] := If[ n < 1, Boole[n == 0], -24 Sum[ (-1)^(n + d) n / d, { d, Divisors[ n]}]]; (* Michael Somos, Aug 21 2014 *) a[ n_] := If[ n < 1, Boole[n == 0], -24 DivisorSum[ n, (-1)^(n + #) n / # &]]; (* Michael Somos, Aug 21 2014 *) PROG (PARI) {a(n) = if( n<1, n==0, (-1)^n * 24 * sumdiv(n, d, d%2*d))}; /* Michael Somos, May 29 2005 */ (MAGMA) A := Basis( ModularForms( Gamma0(4), 2), 46); A[1] - 24*A[2]; /* Michael Somos, Aug 21 2014 */ CROSSREFS Cf. A004011. Sequence in context: A040553 A022358 A122505 * A004011 A056465 A056455 Adjacent sequences:  A103637 A103638 A103639 * A103641 A103642 A103643 KEYWORD sign,look AUTHOR Ralf Stephan, Feb 18 2005 STATUS approved

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

Last modified February 21 23:41 EST 2020. Contains 332113 sequences. (Running on oeis4.)