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A080966
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Expansion of theta_4(q^2)theta_2(q)^2/(4q^(1/2)) in powers of q.
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1
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1, 2, -1, -2, 0, -4, -1, 2, -4, 2, 4, 2, 1, -2, 4, 2, 4, 0, -4, 0, -3, 4, -4, -4, 0, -2, 0, -6, 0, 2, -1, -4, 4, -4, -4, 8, 4, 6, 0, 2, -8, 0, 7, 2, 4, 2, 4, 0, 0, -6, 4, 0, -4, 0, 0, 0, 1, -6, -4, 4, -8, -2, -4, 4, 0, 2, -4, -6, 0, -2, 4, -8, 1, 2, 0, 0, 4, 4, 4, -2, 4, 6, 0, -2, 0, -4, -8, 10, 8, 8, -1, 4, 4, 2, -4, -4, -8, 6, 4, -6, 8, -6, 4, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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
| G.f.: Product_{k>0} (1+x^k)^2*(1-x^(2k))^3/(1+x^(2k)).
Expansion of f(-q^4)f(q)^2 in powers of q where f(-q)=f(-q,-q^2) is a Ramanujan theta function.
Expansion of q^(-1/4)eta(q^2)^6/(eta(q)^2*eta(q^4)) in powers of q.
Euler transform of period-4 sequence [2,-4,2,-3,...].
G.f.: Product_{k>0} (1-x^(2k))^3*(1+x^k)^2/(1+x^(2k)).
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EXAMPLE
| q +2*q^5 -q^9 -2*q^13 -4*q^21 -q^25 +2*q^29 -4*q^33 +...
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^6/eta(x+A)^2/eta(x^4+A), n))}
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CROSSREFS
| 2a(n)=A080964(4n+1)=2*A072071(4n+1)-A072070(4n+1).
Sequence in context: A138498 A050319 A132456 * A187150 A023895 A070963
Adjacent sequences: A080963 A080964 A080965 * A080967 A080968 A080969
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Feb 28 2003
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