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Search: id:A080963
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| A080963 |
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Expansion of theta_3(q)theta_3(q^2)theta_4(q^8) in powers of q. |
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+0
4
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| 1, 2, 2, 4, 2, 0, 4, 0, 0, 2, -4, -4, 0, 0, -8, 0, -2, -8, 6, -4, -8, 0, 4, 0, 0, -6, -12, 0, 0, 0, -8, 0, -4, 8, 8, -8, 10, 0, 12, 0, 0, 0, -8, 12, 0, 0, -8, 0, 8, 2, 14, 8, -8, 0, 16, 0, 0, 8, -4, 4, 0, 0, -16, 0, 6, 0, 16, -4, 16, 0, 8, 0, 0, 8, -20, -4, 0, 0, -8, 0, -8, -6, 8, 4, -16, 0, 20, 0, 0, -8, -20, -8, 0, 0, -16, 0, -8
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(16n+5)=a(16n+7)=a(16n+8)=a(16n+12)=a(16n+13)=a(16n+15)=0.
Expansion of (eta(q^2)eta(q^4))^3/(eta(q)^2*eta(q^16)) in powers of q.
Euler transform of period-16 sequence [2,-1,2,-4,2,-1,2,-4,2,-1,2,-4,2,-1,2,-3,...].
Expansion of phi(q)phi(q^2)phi(-q^8) in powers of q where phi() is a Ramanujan theta function.
G.f.: Product_{k>0} (1+x^k)^2*(1-x^(2k))*(1-x^(4k))^2/((1+x^(4k))*(1+x^(8k))) . - Michael Somos Feb 16 2006
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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)*eta(x^4+A))^3/(eta(x+A)^2*eta(x^16+A)), n))}
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CROSSREFS
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a(n)=2*A080918(n)-A080917(n). a(2n+1)=2*A034950(n).
Sequence in context: A105478 A114427 A129355 this_sequence A033715 A082564 A133692
Adjacent sequences: A080960 A080961 A080962 this_sequence A080964 A080965 A080966
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Feb 28 2003
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