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Search: id:A095813
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| A095813 |
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Expansion of (eta(q)eta(q^10)^5)/(eta(q^2)eta(q^5)^5) in powers of q. |
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+0
5
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| 1, -1, 0, -1, 1, 4, -4, -1, -3, 3, 12, -12, -2, -8, 8, 31, -30, -5, -20, 19, 72, -68, -12, -44, 41, 154, -144, -24, -90, 84, 312, -289, -48, -178, 164, 603, -554, -92, -336, 307, 1122, -1024, -168, -612, 557, 2024, -1836, -300, -1087, 983, 3552, -3206, -522, -1880, 1692, 6088, -5472, -886, -3180
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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G.f. A(x) satisfies 0=f(A(x),A(x^2)) where f(u,v)=u^2-v+2uv+4uv^2.
G.f. A(x) satisfies A(x^2)=-A(x)A(-x).
G.f. A(q) = q chi(-q)/chi(-q^5)^5 = (1-(phi(-q)/phi(-q^5))^2)/4 where chi(),phi() are Ramanujan's theta functions and equivalent to eta(q^2)^2*eta(q^5)5 = eta(q)^4*eta(q^5)*eta(q^10)^2 +4eta(q)eta(q^2)eta(q^10)^5.
Euler transform of period 10 sequence [ -1,0,-1,0,4,0,-1,0,-1,0,...].
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FORMULA
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G.f.: x(Prod_{k>0} ((1-x^k)(1-x^(10k))^5)/((1-x^(2k))(1-x^(5k))^5)).
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PROGRAM
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(PARI) a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff(eta(x+A)*eta(x^10+A)^5/eta(x^2+A)/eta(x^5+A)^5, n))
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CROSSREFS
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Sequence in context: A089746 A094884 A053216 this_sequence A138522 A010656 A023401
Adjacent sequences: A095810 A095811 A095812 this_sequence A095814 A095815 A095816
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jun 07 2004
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