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A260163 Expansion of f(x^2)^2 / f(-x) in powers of x where f() is a Ramanujan theta function. 1
1, 1, 4, 5, 8, 12, 17, 24, 36, 48, 65, 88, 116, 152, 200, 257, 328, 420, 532, 668, 840, 1045, 1296, 1604, 1972, 2416, 2952, 3592, 4357, 5272, 6356, 7640, 9168, 10964, 13080, 15576, 18497, 21920, 25932, 30604, 36048, 42392, 49752, 58288, 68184, 79617, 92820 (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

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^(-1/8) * eta(q^4)^6 / (eta(q) * eta(q^2)^2 * eta(q^8)^2) in powers of q.

Euler transform of period 8 sequence [ 1, 3, 1, -3, 1, 3, 1, -1, ...].

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

EXAMPLE

G.f. = 1 + x + 4*x^2 + 5*x^3 + 8*x^4 + 12*x^5 + 17*x^6 + 24*x^7 + 36*x^8 + ...

G.f. = q + q^9 + 4*q^17 + 5*q^25 + 8*q^33 + 12*q^41 + 17*q^49 + 24*q^57 + ...

MATHEMATICA

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

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^6 / (eta(x + A) * eta(x^2 + A)^2 * eta(x^8 + A)^2), n))};

CROSSREFS

Cf. A132965.

Sequence in context: A188077 A027975 A011980 * A061765 A242274 A297419

Adjacent sequences:  A260160 A260161 A260162 * A260164 A260165 A260166

KEYWORD

nonn

AUTHOR

Michael Somos, Nov 09 2015

STATUS

approved

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Last modified July 23 00:43 EDT 2019. Contains 325228 sequences. (Running on oeis4.)