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 A233673 Expansion of phi(q) * phi(q^9) / phi(q^3)^2 in powers of q where phi() is a Ramanujan theta function. 3
 1, 2, 0, -4, -6, 0, 12, 16, 0, -28, -36, 0, 60, 76, 0, -120, -150, 0, 228, 280, 0, -416, -504, 0, 732, 878, 0, -1252, -1488, 0, 2088, 2464, 0, -3408, -3996, 0, 5460, 6364, 0, -8600, -9972, 0, 13344, 15400, 0, -20424, -23472, 0, 30876, 35346, 0, -46152, -52644 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS G. C. Greubel, Table of n, a(n) for n = 0..2500 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of eta(q^2)^5 * eta(q^3)^4 * eta(q^12)^4 * eta(q^18)^5 / (eta(q)^2 * eta(q^4)^2 * eta(q^6)^10 * eta(q^9)^2 * eta(q^36)^2) in powers of q. Euler transform of period 36 sequence [ 2, -3, -2, -1, 2, 3, 2, -1, 0, -3, 2, 1, 2, -3, -2, -1, 2, 0, 2, -1, -2, -3, 2, 1, 2, -3, 0, -1, 2, 3, 2, -1, -2, -3, 2, 0, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = f(t) where q = exp(2 Pi i t). a(n) = 2 * A233670(n) unless n=0. EXAMPLE G.f. = 1 + 2*q - 4*q^3 - 6*q^4 + 12*q^6 + 16*q^7 - 28*q^9 - 36*q^10 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q] EllipticTheta[ 3, 0, q^9] / EllipticTheta[ 3, 0, q^3]^2, {q, 0, n}]; (* Michael Somos, Aug 27 2015 *) PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^3 + A)^4 * eta(x^12 + A)^4 * eta(x^18 + A)^5 / (eta(x + A)^2 * eta(x^4 + A)^2 * eta(x^6 + A)^10 * eta(x^9 + A)^2 * eta(x^36 + A)^2), n))}; CROSSREFS Cf. A233670. Sequence in context: A096984 A213723 A104601 * A319931 A192133 A244109 Adjacent sequences: A233670 A233671 A233672 * A233674 A233675 A233676 KEYWORD sign AUTHOR Michael Somos, Dec 14 2013 STATUS approved

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Last modified December 1 03:32 EST 2023. Contains 367468 sequences. (Running on oeis4.)