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A255317 Expansion of psi(-x^3)^2 / chi(-x) in powers of x where psi(), chi() are Ramanujan theta functions. 7
1, 1, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 2, 2, 0, 1, 1, 2, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of psi(x^6) * f(x, x^2) in powers of x where psi(), f() are Ramanujan theta functions.

Expansion of q^(-19/24) * eta(q^2) * eta(q^3)^2 * eta(q^12)^2 / (eta(q) * eta(q^6)^2) in powers of q.

Euler transform of period 12 sequence [ 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, -2, ...].

EXAMPLE

G.f. = 1 + x + x^2 + x^5 + x^6 + 2*x^7 + x^8 + x^11 + x^12 + x^13 + ...

G.f. = q^19 + q^43 + q^67 + q^139 + q^163 + 2*q^187 + q^211 + q^283 + ...

MATHEMATICA

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

CROSSREFS

Sequence in context: A118229 A172250 A309047 * A309168 A179229 A117201

Adjacent sequences:  A255314 A255315 A255316 * A255318 A255319 A255320

KEYWORD

nonn

AUTHOR

Michael Somos, Feb 21 2015

STATUS

approved

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Last modified June 14 15:19 EDT 2021. Contains 345025 sequences. (Running on oeis4.)