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A215600 Expansion of psi(-x)^2 * f(-x)^6 in powers of x where psi(), f() are Ramanujan theta functions. 4
1, -8, 22, -16, -27, 40, -18, 80, -94, -40, 0, -48, 359, -80, -130, -320, 0, 160, 214, 400, -230, -152, -594, 416, -343, 240, 518, -400, 0, 200, 830, -592, -396, -776, 0, -400, 1098, 200, 0, 1120, 729, -552, -2068, 272, -1670, 800, 0, 400, 594, 1480, 598, 48 (list; graph; refs; listen; history; text; internal format)
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

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of psi(-x)^8 * chi(-x^2)^6 = f(-x)^8 / chi(-x^2)^2 in powers of x where psi(), chi(), f() are Ramanujan theta functions. - Michael Somos, Sep 03 2013

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

Euler transform of period 4 sequence [ -8, -6, -8, -8, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (32 t)) = 2^15 (t/i)^4 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A225564. - Michael Somos, Sep 03 2013

Convolution square of A215597.

a(2*n) = A215601(n). - Michael Somos, Sep 03 2013

EXAMPLE

1 - 8*x + 22*x^2 - 16*x^3 - 27*x^4 + 40*x^5 - 18*x^6 + 80*x^7 - 94*x^8 + ...

q - 8*q^3 + 22*q^5 - 16*q^7 - 27*q^9 + 40*q^11 - 18*q^13 + 80*q^15 - 94*q^17 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ q]^6 EllipticTheta[ 2, Pi/4, q^(1/2)]^2 / (2 q^(1/4)), {q, 0, n}] (* Michael Somos, Sep 03 2013 *)

a[ n_] := SeriesCoefficient[ QPochhammer[ q]^8 / QPochhammer[ q^2, q^4]^2, {q, 0, n}] (* Michael Somos, Sep 03 2013 *)

PROG

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

CROSSREFS

Cf. A215597, A215601, A225564.

Sequence in context: A019281 A284737 A013630 * A304301 A236917 A064193

Adjacent sequences:  A215597 A215598 A215599 * A215601 A215602 A215603

KEYWORD

sign

AUTHOR

Michael Somos, Aug 16 2012

STATUS

approved

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Last modified February 16 04:34 EST 2019. Contains 320140 sequences. (Running on oeis4.)