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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
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
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
KEYWORD
sign
AUTHOR
Michael Somos, Apr 25 2005
STATUS
approved