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 A281731 #8 Mar 08 2018 03:23:17
%S A281731 1,-1,-2,0,5,0,-10,2,18,0,-32,0,55,-5,-90,0,144,0,-226,10,346,0,-522,
%T A281731 0,777,-18,-1138,0,1648,0,-2362,32,3348,0,-4704,0,6554,-55,-9056,0,
%U A281731 12425,0,-16932,90,22922,0,-30848,0,41282,-144,-54946,0,72768,0,-95914
%N A281731 Expansion of psi(-x) * psi(-x^3) / (phi(x^2) * phi(x^6)) in powers of x where phi(), psi() are Ramanujan theta functions.
%C A281731 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A281731 G. C. Greubel, <a href="/A281731/b281731.txt">Table of n, a(n) for n = 0..1000</a>
%F A281731 Euler transform of period 24 sequence [-1, -2, -2, 2, -1, -4, -1, 0, -2, -2, -1, 4, -1, -2, -2, 0, -1, -4, -1, 2, -2, -2, -1, 0, ...].
%F A281731 Expansion of (phi(q) / phi(q^4) - phi(q^3) / phi(q^12)) / (2*q) in powers of q^2 where phi() is a Ramanujan theta function.
%F A281731 Expansion of (psi(^2) / phi(^2))^2 - x * (psi(x^6) / phi(x^6))^2 in powers of x where phi(), psi() are Ramanujan theta functions.
%F A281731 Expansion of chi(-x) * chi(-x^3) / (chi(x^2)^2 * chi(x^6)^2) = chi(-x) * psi(-x^3) / (chi(x^2)^2 * phi(x^6)) = psi(-x) * chi(-x^3) / (phi(x^2) * chi(x^6)^2) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
%F A281731 Expansion of q^(-1/2) * eta(q) * eta(q^2) * eta(q^3) * eta(q^6) * eta(q^8)^2 * eta(q^24)^2 / (eta(q^4)^4 * eta(q^12)^4) in powers of q.
%F A281731 a(2*n) = - a(6*n + 1) = A079006(n). a(6*n + 3) = a(6*n + 5) = 0.
%e A281731 G.f. = 1 - x - 2*x^2 + 5*x^4 - 10*x^6 + 2*x^7 + 18*x^8 - 32*x^10 + ...
%e A281731 G.f. = q - q^3 - 2*q^5 + 5*q^9 - 10*q^13 + 2*q^15 + 18*q^17 - 32*q^21 + ...
%t A281731 a[ n_] := SeriesCoefficient[ (1/2) x^(-1/2) EllipticTheta[ 2, Pi/4, x^(1/2)] EllipticTheta[ 2, Pi/4, x^(3/2)]/(EllipticTheta[ 3, 0, x^2] EllipticTheta[ 3, 0, x^6]), {x, 0, n}];
%o A281731 (PARI) {a(n) = if( n<0, 0, my(A = x * O(x^n)); polcoeff( eta(x + A) * eta(x^2 + A) * eta(x^3 + A) * eta(x^6 + A) * eta(x^24 + A)^2 / (eta(x^4 + A)^4 * eta(x^12 + A)^4), n))};
%Y A281731 Cf. A079006.
%K A281731 sign
%O A281731 0,3
%A A281731 _Michael Somos_, Jan 28 2017