login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A263993 Expansion of  f(-x, x^2) / f(-x, -x^3)^3 in powers of x where f(, ) is Ramanujan's general theta function. 2
1, 2, 4, 10, 20, 36, 64, 112, 189, 308, 492, 778, 1210, 1844, 2776, 4144, 6114, 8914, 12884, 18484, 26302, 37124, 52040, 72512, 100415, 138196, 189160, 257648, 349184, 470932, 632312, 845472, 1125853, 1493222, 1973060, 2597892, 3408754, 4457600, 5810544 (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  phi(x^3) / (phi(-x) * f(-x^4)^2) in powers of x where phi(), f() are Ramanujan theta functions.

Expansion of q^(1/3) * eta(q^2) * eta(q^6)^5 / (eta(q)^2 * eta(q^3)^2 * eta(q^4)^2 * eta(q^12)^2) in powers of q.

Euler transform of period 12 sequence [ 2, 1, 4, 3, 2, -2, 2, 3, 4, 1, 2, 2, ...].

a(n) = A133637(3*n - 1).

EXAMPLE

G.f. = 1 + 2*x + 4*x^2 + 10*x^3 + 20*x^4 + 36*x^5 + 64*x^6 + 112*x^7 + ...

G.f. = 1/q + 2*q^2 + 4*q^5 + 10*q^8 + 20*q^11 + 36*q^14 + 64*q^17 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, x^3] / (EllipticTheta[ 4, 0, x] QPochhammer[ x^4]^2), {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^6 + A)^5 / (eta(x + A)^2 * eta(x^3 + A)^2 * eta(x^4 + A)^2 * eta(x^12 + A)^2), n))};

CROSSREFS

Cf. A133637.

Sequence in context: A236001 A127392 A258092 * A189585 A239346 A004647

Adjacent sequences:  A263990 A263991 A263992 * A263994 A263995 A263996

KEYWORD

nonn

AUTHOR

Michael Somos, Oct 31 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 July 22 21:28 EDT 2019. Contains 325227 sequences. (Running on oeis4.)