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 A233672 Expansion of psi(q) * phi(-q^18) * f(-q^6) / f(q^3)^3 in powers of q where phi(), psi(), f() are Ramanujan theta functions. 2
 1, 1, 0, -2, -3, 0, 6, 8, 0, -14, -18, 0, 30, 38, 0, -60, -75, 0, 114, 140, 0, -208, -252, 0, 366, 439, 0, -626, -744, 0, 1044, 1232, 0, -1704, -1998, 0, 2730, 3182, 0, -4300, -4986, 0, 6672, 7700, 0, -10212, -11736, 0, 15438, 17673, 0, -23076, -26322, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of eta(q^2)^2 * eta(q^3)^3 * eta(q^12)^3 * eta(q^18)^2 / (eta(q) * eta(q^6)^8 * eta(q^36)) in powers of q. Euler transform of period 36 sequence [ 1, -1, -2, -1, 1, 4, 1, -1, -2, -1, 1, 1, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 1, 1, -1, -2, -1, 1, 4, 1, -1, -2, -1, 1, 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) = A223670(n) unless n=0. EXAMPLE G.f. = 1 + q - 2*q^3 - 3*q^4 + 6*q^6 + 8*q^7 - 14*q^9 - 18*q^10 + ... MATHEMATICA eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[eta[q^2]^2 *eta[q^3]^3*eta[q^12]^3*eta[q^18]^2/(eta[q]*eta[q^6]^8*eta[q^36]), {q, 0, 50}], q] (* G. C. Greubel, Aug 08 2018 *) PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^12 + A)^3 * eta(x^18 + A)^2 / (eta(x + A) * eta(x^6 + A)^8 * eta(x^36 + A)), n))}; CROSSREFS Cf. A233670. Sequence in context: A199601 A231602 A097287 * A233670 A089134 A349776 Adjacent sequences: A233669 A233670 A233671 * A233673 A233674 A233675 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.)