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 A258279 Expansion of psi(q)^2 * chi(-q^3)^2 in powers of q where psi(), chi() are Ramanujan theta functions. 5
 1, 2, 1, 0, -2, -2, 0, 0, 1, -4, -4, 0, 0, 4, 0, 0, -2, -2, 4, 0, 2, 0, 0, 0, 0, 6, 2, 0, 0, -2, 0, 0, 1, 0, -4, 0, 4, 4, 0, 0, -4, -2, 0, 0, 0, -8, 0, 0, 0, 2, 3, 0, -4, -2, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, -2, -4, 0, 0, 2, 0, 0, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2 (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..1000 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of eta(q^2)^4 * eta(q^3)^2 / (eta(q)^2 * eta(q^6)^2) in powers of q. Euler transform of period 6 sequence [ 2, -2, 0, -2, 2, -2, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (72 t)) = 36 (t/i) g(t) where q = exp(2 Pi i t) and g(t) is the g.f. for A002175. G.f.: Product_{k>0} (1 - x^(2*k))^2 / (1 - x^k + x^(2*k))^2. Convolution square of A089810. a(2*n) = A258228(n). a(3*n + 1) = 2 * A258277(n). a(3*n + 2) = A258278(n). a(4*n + 3) = 0. a(6*n + 2) = A122865(n). a(6*n + 4) = -2 * A122856(n). a(12*n + 1) = 2 * A002175(n). a(12*n + 5) = -2 * A121444(n). a(18*n) = A004018(n). a(18*n + 3) = a(18*n + 6) = a(18*n + 12) = 0. EXAMPLE G.f. = 1 + 2*q + q^2 - 2*q^4 - 2*q^5 + q^8 - 4*q^9 - 4*q^10 + 4*q^13 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, Pi/6, q]^2, {q, 0, n}]; 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) / (eta(x + A) * eta(x^6 + A)))^2, n))}; CROSSREFS Cf. A002175, A004018, A089810, A121444, A258277, A258278. Sequence in context: A112178 A134663 A000925 * A258292 A003985 A328948 Adjacent sequences: A258276 A258277 A258278 * A258280 A258281 A258282 KEYWORD sign AUTHOR Michael Somos, May 25 2015 STATUS approved

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Last modified July 15 19:27 EDT 2024. Contains 374334 sequences. (Running on oeis4.)