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Search: id:A116597
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| A116597 |
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Expansion of theta_3(q)*theta_4(q^4)^2 in powers of q. |
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2
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| 1, 2, 0, 0, -2, -8, 0, 0, -4, 10, 0, 0, 8, -8, 0, 0, 6, 16, 0, 0, -8, -16, 0, 0, -8, 10, 0, 0, 0, -24, 0, 0, 12, 16, 0, 0, -10, -8, 0, 0, -8, 32, 0, 0, 24, -24, 0, 0, 8, 18, 0, 0, -8, -24, 0, 0, -16, 16, 0, 0, 0, -24, 0, 0, 6, 32, 0, 0, -16, -32, 0, 0, -12, 16, 0, 0, 24, -32, 0, 0, 24, 34, 0, 0, -16, -16, 0, 0, -8, 48
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of phi(q)*phi(-q^4)^2 in powers of q where phi() is a Ramanujan theta function.
Expansion of eta(q^2)^5*(eta(q^4)/(eta(q)*eta(q^8)))^2 in powers of q.
Euler transform of period 8 sequence [2,-3,2,-5,2,-3,2,-3,...].
a(4n+2)=a(4n+3)=0.
G.f.: theta_3(q)*theta_4(q^4)^2 = Product_{k>0} (1-x^(2k))^3*((1+x^k)/(1+x^(4k)))^2.
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^5*(eta(x^4+A)/eta(x+A)/eta(x^8+A))^2, n))}
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CROSSREFS
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a(n)=A080963(4n). a(4n+1)=(-1)^n*A005876(n).
Adjacent sequences: A116594 A116595 A116596 this_sequence A116598 A116599 A116600
Sequence in context: A127862 A024690 A066209 this_sequence A019263 A091731 A127648
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Feb 18 2006
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