A279365 - OEIS

A279365

Expansion of phi(-x)^2 / chi(-x^5) in powers of x where psi(), chi() are Ramanujan theta functions.

1, -4, 4, 0, 4, -7, -4, 4, 4, 0, 1, -4, 4, -4, 0, 2, -4, 0, 0, 4, 2, -4, 0, 4, 0, -1, 0, 4, -4, -4, -8, 0, 4, 4, 4, 1, 0, 0, 0, 4, -2, 0, -4, 0, -4, 0, -4, 0, 0, 4, 2, 4, 0, -4, -4, 8, 0, 4, 0, -4, -1, 0, -4, 0, 0, 2, 0, -4, 4, 0, -2, 4, -4, 0, 0, -1, 0, 0, -4

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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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-5/24) * eta(q)^4 * eta(q^10) / (eta(q^2)^2 * eta(q^5)) in powers of q.

Euler transform of period 10 sequence [ -4, -2, -4, -2, -3, -2, -4, -2, -4, -2, ...].

EXAMPLE

G.f. = 1 - 4*x + 4*x^2 + 4*x^4 - 7*x^5 - 4*x^6 + 4*x^7 + 4*x^8 + ...

G.f. = q^5 - 4*q^29 + 4*q^53 + 4*q^101 - 7*q^125 - 4*q^149 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x]^2 / QPochhammer[ x^5, x^10], {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^4 * eta(x^10 + A) / (eta(x^2 + A)^2 * eta(x^5 + A)), n))};

(PARI) lista(nn) = {q='q+O('q^nn); Vec(eta(q)^4*eta(q^10)/(eta(q^2)^2*eta(q^5)))} \\ Altug Alkan, Mar 21 2018

CROSSREFS

Sequence in context: A155836 A337398 A245971 * A164613 A104794 A004018

Adjacent sequences: A279362 A279363 A279364 * A279366 A279367 A279368

KEYWORD

sign

AUTHOR

Michael Somos, Dec 10 2016

STATUS

approved