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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A146164 Expansion of f(-x^4) * chi(x^5) / f(-x^5) in powers of x where f(), chi() are Ramanujan theta functions. 4
1, 0, 0, 0, -1, 2, 0, 0, -1, -2, 3, 0, 0, -2, -3, 6, 0, 0, -3, -6, 11, 0, 0, -6, -10, 18, 0, 0, -9, -16, 28, 0, 0, -14, -25, 44, 0, 0, -22, -38, 67, 0, 0, -32, -57, 100, 0, 0, -48, -84, 146, 0, 0, -70, -121, 210, 0, 0, -99, -172, 299, 0, 0, -140, -243, 420, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

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 = 0..1000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(1/4) * eta(q^4) * eta(q^10)^2 / (eta(q^5)^2 * eta(q^20)) in powers of q.

Euler transform of period 20 sequence [ 0, 0, 0, -1, 2, 0, 0, -1, 0, 0, 0, -1, 0, 0, 2, -1, 0, 0, 0, 0, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = (5/4)^(1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A146162.

a(5*n + 1) = a(5*n + 2) = 0.

a(n) = A138532(2*n + 1). a(5*n + 4) = - A146163(n).

Convolution inverse of A146165.

EXAMPLE

G.f. = 1 - x^4 + 2*x^5 - x^8 - 2*x^9 + 3*x^10 - 2*x^13 - 3*x^14 + 6*x^15 + ...

G.f. = 1/q - q^15 + 2*q^19 - q^31 - 2*q^35 + 3*q^39 - 2*q^51 - 3*q^55 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^4] QPochhammer[ -x^5, x^10] / QPochhammer[ x^5], {x, 0, n}]; (* Michael Somos, Sep 03 2015 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^10 + A)^2 / (eta(x^5 + A)^2 * eta(x^20 + A)), n))};

CROSSREFS

Cf. A138532, A146162, A146163, A146165.

Sequence in context: A111755 A144528 A290694 * A263141 A051510 A320781

Adjacent sequences:  A146161 A146162 A146163 * A146165 A146166 A146167

KEYWORD

sign

AUTHOR

Michael Somos, Oct 27 2008, Nov 10 2008

EXTENSIONS

Edited by N. J. A. Sloane, Nov 21 2008 at the suggestion of R. J. Mathar

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 15 02:31 EDT 2020. Contains 335762 sequences. (Running on oeis4.)