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 A228746 #19 Feb 16 2025 08:33:20
%S A228746 1,120,24,480,24,720,96,960,24,1560,144,1440,96,1680,192,2880,24,2160,
%T A228746 312,2400,144,3840,288,2880,96,3720,336,4800,192,3600,576,3840,24,
%U A228746 5760,432,5760,312,4560,480,6720,144,5040,768,5280,288,9360,576,5760,96,6840
%N A228746 Expansion of 8 * phi(q)^4 - 7 * phi(-q)^4 in powers of q where phi() is a Ramanujan theta function.
%C A228746 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%C A228746 Convolution with A005875 is A004008.
%H A228746 G. C. Greubel, <a href="/A228746/b228746.txt">Table of n, a(n) for n = 0..2500</a>
%H A228746 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>, 2019.
%H A228746 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>.
%F A228746 a(n) = 120 * b(n) with b() multiplicative where b(2^e) = 1/5 if e>1, b(p^e) = b(p) * b(p^(e-1)) - p * b(p^(e-2)), if p>2.
%F A228746 G.f. is a period 1 Fourier series which satisfies f(-1 / (4 t)) = 32 (t/i)^2 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A228745.
%F A228746 G.f.: 8 * (Sum_{k in Z} x^k^2)^4 - 7 * (Sum_{k in Z} (-x)^k^2)^4 .
%F A228746 a(2*n) = A004011(n). a(2*n + 1) = 120 * A008438(n).
%F A228746 Sum_{k=1..n} a(k) ~ c * n^2, where c = 4*Pi^2 = 39.478417... (A212002). - _Amiram Eldar_, Dec 29 2023
%e A228746 G.f. = 1 + 120*q + 24*q^2 + 480*q^3 + 24*q^4 + 720*q^5 + 96*q^6 + 960*q^7 + ...
%t A228746 a[ n_] := SeriesCoefficient[ (8 EllipticTheta[ 3, 0, q]^4 - 7 EllipticTheta[ 4, 0, q]^4), {q, 0, n}];
%o A228746 (PARI) {a(n) = my(A); if( n<0, 0, A = sum(k=1, sqrtint(n), 2 * x^k^2, 1 + x * O(x^n)); polcoeff( 8 * A^4 - 7 * subst(A, x, -x)^4, n))};
%o A228746 (Magma) A := Basis( ModularForms( Gamma0(4), 2), 50); A[1] + 120*A[2]; /* _Michael Somos_, Aug 21 2014 */
%Y A228746 Cf. A004008, A004011, A005875, A008438, A212002, A228745.
%Y A228746 Cf. A000122, A000700, A010054, A121373.
%K A228746 nonn,easy
%O A228746 0,2
%A A228746 _Michael Somos_, Sep 02 2013