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A106204
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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.
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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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.
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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))}
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CROSSREFS
| Cf. A007263.
Sequence in context: A063613 A080346 A124026 * A083074 A181869 A141510
Adjacent sequences: A106201 A106202 A106203 * A106205 A106206 A106207
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Apr 25 2005
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