A106204 Expansion of (chi(-q^3)^8 + 16*q^2/ chi(-q^3)^8)^(1/8) in powers of q where chi() is a Ramanujan theta function.

1, 0, 2, -1, -14, 30, 140, -434, -1370, 6579, 13020, -100040, -101611, 1500338, 245954, -22069601, 14502792, 316451640, -480024439, -4385787620, 10970363300, 57983545059, -217649312794, -714104478148, 3986473537118, 7776402179076

Offset

0,3

Comments

Ramanujan theta functions: f(q) := Product_{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} q^(k*(k+1)/2) (A010054), chi(q) := Product_{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 q^(1/8)*((eta(q^3)/ eta(q^6))^8 + 16*(eta(q^6)/ eta(q^3))^8)^(1/8) in powers of q.

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_] := SeriesCoefficient[q^(1/8)*((eta[q^3]/eta[q^6])^8 + 16*(eta[q^6]/eta[q^3])^8)^(1/8), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Mar 07 2018 *)

Prog

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); A=(eta(x^3+A)/eta(x^6+A))^8; polcoeff( (A+16*x^2/A)^(1/8), n))}

Crossrefs

Cf. A000122, A000700, A007263, A010054, A121373.

Sequence in context: A080346 A216445 A124026 * A290603 A083074 A346378

Adjacent sequences: A106201 A106202 A106203 * A106205 A106206 A106207

Keyword

sign

Author

Michael Somos, Apr 25 2005

Status

approved