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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A257400 Expansion of psi(q) * phi(q^2) * chi(-q^3) in powers of q where phi(), psi(), chi() are Ramanujan theta functions. 2
1, 1, 2, 2, -1, 0, -2, 0, 2, 0, 0, -4, -2, 0, 0, 0, -1, -4, 0, 2, 0, 0, -2, 0, -2, 1, 0, -2, 0, 0, 0, 0, 2, 4, -2, 0, 0, 0, 4, 0, 0, -4, 0, 2, 4, 0, 0, 0, -2, 1, 2, 4, 0, 0, 2, 0, 0, 4, 0, -4, 0, 0, 0, 0, -1, 0, -4, 2, 4, 0, 0, 0, 0, 2, 0, 2, -2, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
LINKS
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of eta(q^3) * eta(q^4)^5 / (eta(q) * eta(q^8)^2 * eta(q^6)) in powers of q.
Euler transform of period 24 sequence [1, 1, 0, -4, 1, 1, 1, -2, 0, 1, 1, -4, 1, 1, 0, -2, 1, 1, 1, -4, 0, 1, 1, -2, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = 2592^(1/2) (t/i) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A257399.
a(8*n + 7) = 0.
EXAMPLE
G.f. = 1 + q + 2*q^2 + 2*q^3 - q^4 - 2*q^6 + 2*q^8 - 4*q^11 - 2*q^12 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, q^(1/2)] EllipticTheta[ 3, 0, q^2] QPochhammer[ q^3, q^6] / (2 q^(1/8)), {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A) * eta(x^4 + A)^5 / (eta(x + A) * eta(x^8 + A)^2 * eta(x^6 + A)), n))};
CROSSREFS
Cf. A257399.
Sequence in context: A332813 A323077 A334201 * A328081 A194853 A309866
KEYWORD
sign
AUTHOR
Michael Somos, Apr 21 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 5 17:38 EDT 2024. Contains 375700 sequences. (Running on oeis4.)