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 A145723 Expansion of q^(-1) * f(q) * chi(-q^5) / f(-q^20) in powers of q where f(), chi() are Ramanujan theta functions. 4
 1, 1, -1, 0, 0, -2, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 2, 0, 0, 2, 2, 0, 0, 0, -4, -1, 0, 0, 0, 2, 0, -1, 0, 0, 0, -2, 2, 0, 0, 3, 4, -2, 0, 0, -8, -3, 0, 0, 0, 5, 0, -2, 0, 0, 0, -3, 4, 0, 0, 6, 8, -2, 0, 0, -14, -4, 0, 0, 0, 8, 0, -3, 0, 0, 0, -6, 8, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,6 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 = -1..1000 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of eta(q^2)^3 * eta(q^5) / (eta(q) * eta(q^4) * eta(q^10) * eta(q^20)) in powers of q. Euler transform of period 20 sequence [ 1, -2, 1, -1, 0, -2, 1, -1, 1, -2, 1, -1, 1, -2, 0, -1, 1, -2, 1, 0, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = 20^(1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A145722. a(4*n + 2) = a(5*n + 2) = a(5*n + 3) = 0. a(4*n) = A138527(n). a(4*n + 1) = - A147699(n). Convolution inverse of A145724. EXAMPLE G.f. = 1/q + 1 - q - 2*q^4 - q^5 + q^9 - q^15 + 2*q^16 + 2*q^19 + 2*q^20 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ 1/q QPochhammer[ -q]  QPochhammer[ q^5, q^10] / QPochhammer[ q^20], {q, 0, n}]; (* Michael Somos, Sep 05 2015 *) PROG (PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^5 + A) / (eta(x + A) * eta(x^4 + A) * eta(x^10 + A) * eta(x^20 + A)), n))}; CROSSREFS Cf. A138527, A145722, A145724, A147699. Sequence in context: A339070 A077655 A117886 * A085977 A288424 A127325 Adjacent sequences:  A145720 A145721 A145722 * A145724 A145725 A145726 KEYWORD sign AUTHOR Michael Somos, Nov 06 2008 STATUS approved

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Last modified January 24 12:04 EST 2022. Contains 350536 sequences. (Running on oeis4.)