M. Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
OEIS Server: https://oeis.org/edit/global/2897
M. Somos, <a href="http://somos.crg4.com="/A010815/multiqa010815.htmltxt">Introduction to Ramanujan theta functions</a>
OEIS Server: https://oeis.org/edit/global/2832
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G. C. Greubel, <a href="/A263433/b263433.txt">Table of n, a(n) for n = 0..2500</a>
G.f. is a period 1 Fourier series which satisfies f(-1 / (72 t)) = 15552^(1/2) (t/i)^(1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A263444.
Cf. A005889, A045832, A261426, A263444.
Michael Somos: Added more info.
allocatedExpansion of f(x, x) * f(x^2, x^4)^2 in powers of x where f(, ) is Ramanujan's forgeneral Michaeltheta Somosfunction.
1, 2, 2, 4, 5, 6, 6, 4, 7, 4, 6, 8, 4, 10, 8, 12, 8, 6, 14, 8, 11, 6, 8, 8, 8, 14, 6, 12, 15, 14, 14, 8, 12, 14, 12, 16, 8, 10, 14, 16, 16, 12, 12, 12, 16, 10, 10, 8, 19, 20, 20, 8, 12, 24, 14, 24, 12, 16, 14, 16, 21, 10, 14, 28, 16, 12, 14, 12, 16, 16, 30, 12
0,2
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
M. Somos, <a href="http://somos.crg4.com/multiq.html">Introduction to Ramanujan theta functions</a>
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
Expansion of f(-x^2)^2 * phi(-x^6)^2 / phi(-x) in powers of x where phi(), f() are Ramanujan theta functions.
Expansion of q^(-1/6) * eta(q^2)^3 * eta(q^6)^4 / (eta(q)^2 * eta(q^12)^2) in powers of q.
a(n) = A261426(2*n) = A045832(6*n). 3 * a(n) = A005889(6*n).
G.f. = 1 + 2*x + 2*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 6*x^6 + 4*x^7 + 7*x^8 + ...
G.f. = q + 2*q^7 + 2*q^13 + 4*q^19 + 5*q^25 + 6*q^31 + 6*q^37 + 4*q^43 + ...
a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^2 EllipticTheta[ 4, 0, x^6]^2 / EllipticTheta[ 4, 0, x], {x, 0, n}];
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^6 + A)^4 / (eta(x + A)^2 * eta(x^12 + A)^2), n))};
Cf. A005889, A045832, A261426.
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Michael Somos, Oct 18 2015