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A131123
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Expansion of (q^-1)* (chi(-q^4)/ chi(-q))^8 in powers of q where chi() is a Ramanujan theta function.
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2
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1, 8, 36, 128, 386, 1024, 2488, 5632, 12031, 24576, 48308, 91904, 170110, 307200, 542872, 941056, 1602819, 2686976, 4439688, 7238272, 11657090, 18561024, 29242240, 45617664, 70507772, 108036096, 164192188, 247620352, 370726652
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,2
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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 (eta(q^2)* eta(q^4)/( eta(q)* eta(q^8) ))^8 in powers of q.
Euler transform of period 8 sequence [ 8, 0, 8, -8, 8, 0, 8, 0, ...].
G.f. A(x) satisfies 0= f(A(x), A(x^2), A(x^4)) where f(u, v, w)= 16* (1-v*w)* (1-v*u) -(v-u^2)* (v-w^2).
G.f. is Fourier series of a weight 0 level 8 modular form. f(-1/(8 t)) = f(t) where q = exp(2 pi i t).
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EXAMPLE
| 1/q + 8 + 36*q + 128*q^2 + 386*q^3 + 1024*q^4 + 2488*q^5 + 5632*q^6 + ...
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PROG
| (PARI) {a(n)= local(A); if(n<-1, 0, n++; A= x*O(x^n); polcoeff( (eta(x^2+A) *eta(x^4+A)/ eta(x+A)/ eta(x^8+A))^8, n))}
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CROSSREFS
| A007265(n)= a(n) unless n=0.
Sequence in context: A145136 A144901 A054470 * A055910 A022573 A014477
Adjacent sequences: A131120 A131121 A131122 * A131124 A131125 A131126
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Jun 15 2007
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