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.
%I A103640 #22 Feb 16 2025 08:32:56
%S A103640 1,-24,24,-96,24,-144,96,-192,24,-312,144,-288,96,-336,192,-576,24,
%T A103640 -432,312,-480,144,-768,288,-576,96,-744,336,-960,192,-720,576,-768,
%U A103640 24,-1152,432,-1152,312,-912,480,-1344,144,-1008,768,-1056,288,-1872
%N A103640 Expansion of theta_4(q)^4 - theta_2(q)^4, where theta_2 and theta_4 are the Jacobi theta series.
%C A103640 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A103640 Seiichi Manyama, <a href="/A103640/b103640.txt">Table of n, a(n) for n = 0..10000</a>
%H A103640 C. Pache, <a href="http://arXiv.org/abs/math.CO/0502313">Shells of selfdual lattices viewed as spherical designs</a>
%H A103640 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A103640 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EisensteinSeries.html">Eisenstein Series</a>
%H A103640 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A103640 G.f.: theta_4(q)^4 - theta_2(q)^4. - _Michael Somos_, May 29 2005
%F A103640 a(n) = (-1)^n * A004011(n). - _Michael Somos_, Jun 01 2012
%F A103640 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
%e A103640 G.f. = 1 - 24*q + 24*q^2 - 96*q^3 + 24*q^4 - 144*q^5 + 96*q^6 - 192*q^7 + ...
%t A103640 a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q]^4 - EllipticTheta[ 2, 0, q]^4, {q, 0, n}]; (* _Michael Somos_, Jun 01 2012 *)
%t A103640 a[ n_] := With[{m = InverseEllipticNomeQ @x}, SeriesCoefficient[(1 - 2 m) (EllipticK[m] / (Pi/2))^2, {x, 0, n}]]; (* _Michael Somos_, Aug 21 2014 *)
%t A103640 a[ n_] := If[ n < 1, Boole[n == 0], -24 Sum[ (-1)^(n + d) n / d, { d, Divisors[ n]}]]; (* _Michael Somos_, Aug 21 2014 *)
%t A103640 a[ n_] := If[ n < 1, Boole[n == 0], -24 DivisorSum[ n, (-1)^(n + #) n / # &]]; (* _Michael Somos_, Aug 21 2014 *)
%o A103640 (PARI) {a(n) = if( n<1, n==0, (-1)^n * 24 * sumdiv(n, d, d%2*d))}; /* _Michael Somos_, May 29 2005 */
%o A103640 (Magma) A := Basis( ModularForms( Gamma0(4), 2), 46); A[1] - 24*A[2]; /* _Michael Somos_, Aug 21 2014 */
%Y A103640 Cf. A004011.
%K A103640 sign,look
%O A103640 0,2
%A A103640 _Ralf Stephan_, Feb 18 2005