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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A262614 Expansion of phi(-x^3) * f(-x, -x^5) / psi(x) in powers of x where phi(), psi(), f(, ) are Ramanujan theta functions. 3
1, -2, 2, -5, 9, -12, 16, -23, 36, -47, 60, -84, 115, -149, 188, -245, 321, -406, 505, -641, 813, -1007, 1237, -1533, 1901, -2321, 2816, -3437, 4191, -5055, 6068, -7307, 8792, -10501, 12490, -14886, 17720, -20975, 24755, -29236, 34492, -40522, 47486, -55666 (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 f(-x^3)^3 / (f(x, x^2) * psi(x)) in powers of x where psi(), f(, ) are Ramanujan theta functions.

Expansion of q^(-5/24) * eta(q)^2 * eta(q^3) * eta(q^6) / eta(q^2)^3 in powers of q.

Euler transform of period 6 sequence [ -2, 1, -3, 1, -2, -1, ...].

a(n) = A053269(3*n + 1).

a(n) ~ (-1)^n * exp(sqrt(n/2)*Pi) / (6*sqrt(n)). - Vaclav Kotesovec, Apr 17 2016

EXAMPLE

G.f. = 1 - 2*x + 2*x^2 - 5*x^3 + 9*x^4 - 12*x^5 + 16*x^6 - 23*x^7 +

G.f. = q^5 - 2*q^29 + 2*q^53 - 5*q^77 + 9*q^101 - 12*q^125 + 16*q^149 - 23*q^173 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ 2 x^(1/8) QPochhammer[ x^3]^3 QPochhammer[ x, x^2] / (EllipticTheta[ 4, 0, x^3] EllipticTheta[ 2, 0, x^(1/2)]), {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^3 + A) * eta(x^6 + A) / eta(x^2 + A)^3, n))};

CROSSREFS

Cf. A053269.

Sequence in context: A275266 A223387 A278386 * A184296 A131133 A096569

Adjacent sequences:  A262611 A262612 A262613 * A262615 A262616 A262617

KEYWORD

sign

AUTHOR

Michael Somos, Apr 17 2016

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 20 11:59 EDT 2018. Contains 316379 sequences. (Running on oeis4.)