A215594 Expansion of f(-x, -x^4) / f(x, x^4) in powers of x where f(,) is Ramanujan's two-variable theta function.

1, -2, 2, -2, 0, 2, -4, 6, -4, 0, 6, -12, 14, -10, 0, 14, -26, 30, -22, 0, 28, -52, 60, -42, 0, 54, -100, 112, -78, 0, 100, -180, 202, -140, 0, 174, -314, 350, -240, 0, 296, -532, 588, -402, 0, 492, -876, 966, -658, 0, 794, -1412, 1550, -1050, 0, 1260, -2232

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

Euler transform of period 10 sequence [ -2, 1, 0, -2, 0, -2, 0, 1, -2, 0, ...].

a(5*n + 4) = 0.

Example

1 - 2*x + 2*x^2 - 2*x^3 + 2*x^5 - 4*x^6 + 6*x^7 - 4*x^8 + 6*x^10 - 12*x^11 + ...

Mathematica

f[x_, y_] := QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; A215594[n_] := SeriesCoefficient[f[-x, -x^4]/f[x, x^4], {x, 0, n}]; Table[A215594[n], {n, 0, 50}] (* G. C. Greubel, Jun 18 2017 *)

Prog

(PARI) {a(n) = local(A, s); if( n<0, 0, A = x * O(x^n); s = sqrtint( 40*n + 9); polcoeff( sum( k=(-s + 6)\10, (s - 3)\10, (-1)^k *  x^((5*k + 3)*k/2), A) / sum( k=(-s + 6)\10, (s - 3)\10,  x^((5*k + 3)*k/2), A), n))}

Crossrefs

Sequence in context: A264136 A274850 A349437 * A230291 A338434 A059288

Adjacent sequences: A215591 A215592 A215593 * A215595 A215596 A215597

Keyword

sign

Author

Michael Somos, Aug 16 2012

Status

approved