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A132040
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Expansion of q^-1* (chi(-q)* chi(-q^5))^4 in powers of q where chi() is a Ramanujan theta function.
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1
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1, -4, 6, -8, 17, -32, 54, -80, 116, -192, 290, -408, 585, -832, 1192, -1648, 2237, -3072, 4156, -5576, 7414, -9824, 12964, -16896, 22002, -28544, 36794, -47184, 60185, -76736, 97388, -122864, 154615, -194048, 242904, -302800, 376271, -466720, 577176, -711840, 875611
(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)* eta(q^5)/( eta(q^2)* eta(q^10)))^4 in powers of q.
Euler transform of period 10 sequence [ -4, 0, -4, 0, -8, 0, -4, 0, -4, 0, ...].
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= v*(u^2 -v) +8*u* (v +2).
G.f. is a Fourier series which satisfies f(-1/(10 t)) = 16/ f(t) where q = exp(2 pi i t).
G.f.: (Product_{k>0} (1+x^k)* (1+x^(5k)))^-4.
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EXAMPLE
| 1/q - 4 + 6*q - 8*q^2 + 17*q^3 - 32*q^4 + 54*q^5 - 80*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+A)* eta(x^5+A)/ eta(x^2+A)/ eta(x^10+A))^4, n))}
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CROSSREFS
| A058098(n)= a(n) unless n=0. a(n)= (-1)^n* A112158(n) unless n=0.
Sequence in context: A185292 A022599 A112160 * A114315 A058238 A073437
Adjacent sequences: A132037 A132038 A132039 * A132041 A132042 A132043
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Aug 07 2007
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