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!)
A263074 Expansion of phi(-x) / (chi(-x^3) * chi(-x^5)) in powers of x where phi(), chi() are Ramanujan theta functions. 1
1, -2, 0, 1, 0, 1, -1, 0, 1, 0, -1, -1, 0, 1, 0, 1, -3, 0, 2, 0, 1, -1, 0, 2, 0, 0, -3, 0, 1, 0, 2, -4, 0, 2, 0, 1, -3, 0, 3, 0, 1, -4, 0, 2, 0, 3, -6, 0, 4, 0, 4, -6, 0, 4, 0, 1, -7, 0, 4, 0, 3, -9, 0, 5, 0, 4, -8, 0, 6, 0, 3, -10, 0, 6, 0, 6, -13, 0, 8, 0, 5 (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

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-1/3) * eta(q)^2 * eta(q^6) * eta(q^10) / (eta(q^2) * eta(q^3) * eta(q^5)) in powers of q.

Euler transform of period 30 sequence [ -2, -1, -1, -1, -1, -1, -2, -1, -1, -1, -2, -1, -2, -1, 0, -1, -2, -1, -2, -1, -1, -1, -2, -1, -1, -1, -1, -1, -2, -1, ...].

G.f.: Product_{k>0} (1 + x^(3*k)) * (1 + x^(5*k)) * (1 - x^k) / (1 + x^k).

Convolution inverse is A100823.

a(5*n + 2) = a(5*n + 4) = 0. a(5*n + 3) = A263073(n).

EXAMPLE

G.f. = 1 - 2*x + x^3 + x^5 - x^6 + x^8 - x^10 - x^11 + x^13 + x^15 + ...

G.f. = q - 2*q^4 + q^10 + q^16 - q^19 + q^25 - q^31 - q^34 + q^40 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x] / (QPochhammer[ x^3, x^6] QPochhammer[ x^5, x^10]), {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^6 + A) * eta(x^10 + A) / (eta(x^2 + A) * eta(x^3 + A) * eta(x^5 + A)), n))};

CROSSREFS

Cf. A100823, A263073.

Sequence in context: A319660 A285726 A285005 * A281772 A082886 A287179

Adjacent sequences:  A263071 A263072 A263073 * A263075 A263076 A263077

KEYWORD

sign

AUTHOR

Michael Somos, Oct 08 2015

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 August 6 12:33 EDT 2020. Contains 336246 sequences. (Running on oeis4.)