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 A258590 Expansion of psi(-x) * psi(-x^6)^2 / f(-x^3) in powers of x where psi(), f() are Ramanujan theta functions. 1
 1, -1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 1, -1, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 2, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, -2, 0, 0, 0, 0, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 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..1000 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of psi(-x) * psi(x^3) / chi(-x^12)^2 = psi(-x) * chi(x^3) * psi(x^12) in powers of x where psi(), chi() are Ramanujan theta functions. Expansion of q^(-3/2) * eta(q) * eta(q^4) * eta(q^6)^2 * eta(q^24)^2 / (eta(q^2) * eta(q^3) * eta(q^12)^2) in powers of q. Euler transform of period 24 sequence [ -1, 0, 0, -1, -1, -1, -1, -1, 0, 0, -1, 0, -1, 0, 0, -1, -1, -1, -1, -1, 0, 0, -1, -2, ...]. 2 * a(n) = A263577(2*n + 3). EXAMPLE G.f. = 1 - x - x^4 + 2*x^9 + x^12 - x^13 - 2*x^16 + 2*x^21 - x^25 - x^28 + ... G.f. = q^3 - q^5 - q^11 + 2*q^21 + q^27 - q^29 - 2*q^35 + 2*q^45 - q^53 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ 2^(-3/2) x^(-13/8) EllipticTheta[ 2, Pi/4, x^(1/2)] EllipticTheta[ 2, Pi/4, x^3]^2 / QPochhammer[ x^3], {x, 0, n}]; a[ n_] := SeriesCoefficient[ 2^(-3/2) x^(-13/8) EllipticTheta[ 2, Pi/4, x^(1/2)] EllipticTheta[ 2, 0, x^6] QPochhammer[ -x^3, x^6], {x, 0, n}]; a[ n_] := SeriesCoefficient[ 2^(-3/2) x^(-1/2) EllipticTheta[ 2, Pi/4, x^(1/2)] EllipticTheta[ 2, 0, x^(3/2)]  QPochhammer[ -x^12, x^12]^2, {x, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^2 * eta(x^24 + A)^2 / (eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)^2), n))}; CROSSREFS Cf. A263577. Sequence in context: A230263 A139354 A124762 * A057558 A284502 A281456 Adjacent sequences:  A258587 A258588 A258589 * A258591 A258592 A258593 KEYWORD sign AUTHOR Michael Somos, Nov 06 2015 STATUS approved

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Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)