The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A145708 Expansion of psi(-q) / psi(-q^5) in powers of q where psi() is a Ramanujan theta function. 3
 1, -1, 0, -1, 0, 1, 0, 0, -1, 0, 2, 0, 0, -1, 0, 2, -1, 0, -2, 0, 3, -2, 0, -3, 0, 5, -2, 0, -3, 0, 6, -2, 0, -4, 0, 8, -3, 0, -6, 0, 11, -5, 0, -8, 0, 14, -6, 0, -10, 0, 18, -6, 0, -12, 0, 22, -9, 0, -16, 0, 28, -13, 0, -21, 0, 36, -14, 0, -25, 0, 44, -16, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 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 q^(1/2) * eta(q) * eta(q^4) * eta(q^10) / (eta(q^2) * eta(q^5) * eta(q^20)) in powers of q. Euler transform of period 20 sequence [ -1, 0, -1, -1, 0, 0, -1, -1, -1, 0, -1, -1, -1, 0, 0, -1, -1, 0, -1, 0, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = 5^(1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A036026. a(5*n + 2) = a(5*n + 4) = 0. G.f.: (Product_{k>0} P(5, x^k) * P(20, x^k))^(-1) where P(n, x) is the n-th cyclotomic polynomial. a(n) = (-1)^n * A138532(n). a(5*n + 3) = - A036026(n). Convolution square is A145740. Convolution inverse is A036026. a(n) = A145723(2*n - 1). a(2*n) = A146164(n). a(2*n + 1) = - A147699(n). - Michael Somos, Sep 06 2015 EXAMPLE G.f. = 1 - x - x^3 + x^5 - x^8 + 2*x^10 - x^13 + 2*x^15 - x^16 - 2*x^18 + ... G.f. = 1/q - q - q^5 + q^9 - q^15 + 2*q^19 - q^25 + 2*q^29 - q^31 - 2*q^35 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ x^(1/2) EllipticTheta[ 2, Pi/4, x^(1/2)] / EllipticTheta[ 2, Pi/4, x^(5/2)], {x, 0, n}]; (* Michael Somos, Sep 06 2015 *) 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^10 + A) / (eta(x^2 + A) * eta(x^5 + A) * eta(x^20 + A)), n))}; CROSSREFS Cf. A036026, A138532, A145723, A145740, A146164. Sequence in context: A346250 A084143 A025888 * A138532 A339445 A065293 Adjacent sequences: A145705 A145706 A145707 * A145709 A145710 A145711 KEYWORD sign AUTHOR Michael Somos, Oct 17 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 10:29 EST 2022. Contains 358493 sequences. (Running on oeis4.)