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A260415 Expansion of f(x, x^2) * f(x^4, x^8) in powers of x where f(,) is Ramanujan's general theta function. 2
1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 2, 1, 0, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 1, 1, 3, 0, 1, 1, 1, 3, 0, 0, 0, 1, 2, 0, 1, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 1, 1, 3, 0, 1, 0, 1, 3, 2, 1, 2, 0, 2, 0, 1, 1, 0, 2, 1, 1, 0, 2, 1, 0, 2, 1, 1, 0, 1, 1, 1, 0, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

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..2500

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-5/24) * eta(q^2) * eta(q^3)^2 * eta(q^8) * eta(q^12)^2 / (eta(q) * eta(q^4) * eta(q^6) * eta(q^24)) in powers of q.

Euler transform of period 24 sequence [ 1, 0, -1, 1, 1, -1, 1, 0, -1, 0, 1, -2, 1, 0, -1, 0, 1, -1, 1, 1, -1, 0, 1, -2, ...].

EXAMPLE

G.f. = 1 + x + x^2 + x^4 + 2*x^5 + x^6 + x^7 + x^8 + 2*x^9 + x^10 + x^11 + ...

G.f. = q^5 + q^29 + q^53 + q^101 + 2*q^125 + q^149 + q^173 + q^197 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, Pi/4, x] QPochhammer[ x^3]^2 QPochhammer[ -x^6, x^12] / (2^(1/2) x^(1/4) QPochhammer[ x]), {x, 0, n}];

a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^3] EllipticTheta[ 4, 0, x^12] / (QPochhammer[ x, x^2] QPochhammer[ x^4, x^8]), {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^3 + A)^2 * eta(x^8 + A) * eta(x^12 + A)^2 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^24 + A)), n))};

CROSSREFS

Sequence in context: A221362 A114116 A054532 * A214710 A120888 A031230

Adjacent sequences:  A260412 A260413 A260414 * A260416 A260417 A260418

KEYWORD

sign

AUTHOR

Michael Somos, Jul 27 2015

STATUS

approved

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Last modified April 9 10:32 EDT 2020. Contains 333348 sequences. (Running on oeis4.)