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 A207541 #28 Feb 16 2025 08:33:16
%S A207541 1,4,0,-16,-8,24,0,-32,24,52,0,-48,-32,56,0,-96,24,72,0,-80,-48,128,0,
%T A207541 -96,96,124,0,-160,-64,120,0,-128,24,192,0,-192,-104,152,0,-224,144,
%U A207541 168,0,-176,-96,312,0,-192,96,228,0,-288,-112,216,0,-288,192,320,0
%N A207541 Expansion of phi(q)^3 * phi(-q) in powers of q where phi() is a Ramanujan theta function.
%C A207541 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A207541 G. C. Greubel, <a href="/A207541/b207541.txt">Table of n, a(n) for n = 0..1000</a>
%H A207541 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A207541 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A207541 Expansion of phi(-q^4)^4 + 4 * q * psi(-q^2)^4 = phi(q)^3 * phi(-q) = phi(q)^2 * phi(-q^2)^2 = psi(q)^4 * chi(-q^2)^6 = phi(-q^2)^6 / phi(-q)^2 = f(q)^6 / psi(q)^2 = f(q)^4 * chi(-q^2)^2 in powers of q where phi(), psi() are Ramanujan theta functions.
%F A207541 Expansion of (eta(q^2)^7 / (eta(q)^2 * eta(q^4)^3))^2 in powers of q.
%F A207541 Euler transform of period 4 sequence [ 4, -10, 4, -4, ...].
%F A207541 G.f. is a period 1 Fourier series which satisfies f(-1 / (16 t)) = 128 (t/i)^2 g(t) where q = exp(2 Pi i t) and g(t) is g.f. for A112610.
%F A207541 G.f.: Product_{k>0} (1 - x^(2*k))^14 / ((1 - x^k)^4 * (1 - x^(4*k))^6).
%F A207541 a(3*n + 2) = 24 * A208435(n). a(4*n + 2) = 0. a(2*n + 1) = 4 * A121613(n). a(4*n) = A096727(n). a(4*n + 1) = 4 * A112610(n). a(4*n + 3) = -16 * A097723(n). Convolution square of A139093.
%e A207541 1 + 4*q - 16*q^3 - 8*q^4 + 24*q^5 - 32*q^7 + 24*q^8 + 52*q^9 - 48*q^11 + ...
%t A207541 a[n_]:= SeriesCoefficient[EllipticTheta[3, 0, q]^3*EllipticTheta[3, 0, -q], {q, 0, n}]; Table[A207541[n], {n, 0, 50}] (* _G. C. Greubel_, Dec 16 2017 *)
%o A207541 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^7 / (eta(x + A)^2 * eta(x^4 + A)^3))^2, n))}
%Y A207541 Cf. A096727, A097723, A112610, A121613, A139093, A208435.
%K A207541 sign
%O A207541 0,2
%A A207541 _Michael Somos_, Feb 26 2012