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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A260164 Expansion of f(-x^8)^2 / f(-x) in powers of x where f() is a Ramanujan theta function. 1
1, 1, 2, 3, 5, 7, 11, 15, 20, 28, 38, 50, 67, 87, 113, 146, 186, 236, 299, 375, 468, 583, 721, 888, 1093, 1336, 1628, 1980, 2397, 2894, 3487, 4186, 5013, 5991, 7139, 8488, 10073, 11924, 14086, 16613, 19551, 22965, 26934, 31527, 36844, 42994, 50085, 58258 (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

Seiichi Manyama, 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^(-5/8) * eta(q^8)^2 / eta(q) in powers of q.

Euler transform of period 8 sequence [ 1, 1, 1, 1, 1, 1, 1, -1, ...].

2 * a(n) = A132965(2*n + 1).

EXAMPLE

G.f. = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 11*x^6 + 15*x^7 + 20*x^8 + ...

G.f. = q^5 + q^13 + 2*q^21 + 3*q^29 + 5*q^37 + 7*q^45 + 11*q^53 + 15*q^61 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^8]^2 / QPochhammer[ x], {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^8 + A)^2 / eta(x + A), n))};

CROSSREFS

Cf. A010054, A132965.

Sequence in context: A090693 A260794 A277576 * A280938 A049756 A218507

Adjacent sequences:  A260161 A260162 A260163 * A260165 A260166 A260167

KEYWORD

nonn

AUTHOR

Michael Somos, Nov 09 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified January 18 18:45 EST 2018. Contains 297864 sequences.