A117886 Expansion of q^(-2/3)eta(q)eta(q^10)^2/eta(q^5) in powers of q.

1, -1, -1, 0, 0, 2, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, -2, 1, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 1, 1, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0

Offset

0,6

Comments

Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A010054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (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 f(-q) * psi(q^5) in powers of q where f(),psi() are Ramanujan theta functions.

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

G.f.: Product_{k>0} (1-x^k)*(1-x^(5k))*(1+x^(5k))^2.

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-2/3)* eta[q]*eta[q^10]^2/eta[q^5], {q, 0, 50}], q] (* G. C. Greubel, Apr 17 2018 *)

Prog

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^10+A)^2/eta(x^5+A), n))}
(PARI) q='q+O('q^99); Vec(eta(q)*eta(q^10)^2/eta(q^5)) \\ Altug Alkan, Apr 18 2018

Crossrefs

Sequence in context: A339070 A352553 A077655 * A145723 A085977 A288424

Adjacent sequences: A117883 A117884 A117885 * A117887 A117888 A117889

Keyword

sign

Author

Michael Somos, Oct 13 2006; corrected Jul 29 2007

Status

approved