The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A164613 Expansion of (phi(q) / phi(q^9))^2 in powers of q where phi() is a Ramanujan theta function. 2
 1, 4, 4, 0, 4, 8, 0, 0, 4, 0, -8, -16, 0, -8, -32, 0, 4, -8, 0, 16, 56, 0, 16, 96, 0, -4, 24, 0, -32, -152, 0, -32, -252, 0, 8, -64, 0, 56, 368, 0, 56, 600, 0, -16, 144, 0, -96, -832, 0, -92, -1316, 0, 24, -312, 0, 160, 1760, 0, 152, 2736, 0, -40, 640, 0, -252, -3536, 0, -240, -5432, 0, 64, -1248, 0, 392 (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)^5 * eta(q^9)^2 * eta(q^36)^2 / (eta(q)^2 * eta(q^4)^2 * eta(q^18)^5))^2 in powers of q. Euler transform of period 36 sequence [ 4, -6, 4, -2, 4, -6, 4, -2, 0, -6, 4, -2, 4, -6, 4, -2, 4, 0, 4, -2, 4, -6, 4, -2, 4, -6, 0, -2, 4, -6, 4, -2, 4, -6, 4, 0, ...]. a(3*n) = 0 unless n=0. a(3*n + 1) = 4 * A128111(n). a(3*n + 2) = 4 * A164614(n). Convolution square of A139380. EXAMPLE G.f. = 1 + 4*q + 4*q^2 + 4*q^4 + 8*q^5 + 4*q^8 - 8*q^10 - 16*q^11 - 8*q^13 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ (EllipticTheta[ 3, 0, q] / EllipticTheta[ 3, 0, q^9])^2, {q, 0, n}]; (* Michael Somos, Sep 02 2015 *) PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^5 * eta(x^9 + A)^2 * eta(x^36 + A)^2 / (eta(x + A)^2 * eta(x^4 + A)^2 * eta(x^18 + A)^5))^2, n))}; CROSSREFS Cf. A128111, A139380, A164614. Sequence in context: A337398 A245971 A279365 * A104794 A004018 A253185 Adjacent sequences:  A164610 A164611 A164612 * A164614 A164615 A164616 KEYWORD sign AUTHOR Michael Somos, Aug 17 2009 STATUS approved

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

Last modified April 10 07:44 EDT 2021. Contains 342843 sequences. (Running on oeis4.)