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Search: id:A097340
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| A097340 |
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Expansion of (eta(q^2)^2/(eta(q)eta(q^4)))^24 in powers of q. |
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+0
2
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| 1, 24, 276, 2048, 11202, 49152, 184024, 614400, 1881471, 5373952, 14478180, 37122048, 91231550, 216072192, 495248952, 1102430208, 2390434947, 5061476352, 10487167336, 21301241856, 42481784514, 83300614144
(list; graph; listen)
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OFFSET
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-1,2
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COMMENT
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Euler transform of period 4 sequence [24,-24,24,0,...].
G.f. A(x) satisfies 0=f(A(x),A(x^2)) where f(u,v)= uv(u^3+v^3) +(-u^3+48u^2-96u)v^3 +(48u^3+1791u^2+2352u)v^2 +(-96u^3+2352u^2-10496u)v +4096.
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REFERENCES
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S. Ramanujan, Modular Equations and Approximations to pi, pp. 23-39 of Collected Papers of Srinivasa Ramanujan, Ed. G. H. Hardy et al., AMS Chelsea 2000. See page 26.
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LINKS
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T. D. Noe, Table of n, a(n) for n=-1..1000
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FORMULA
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G.f. (1/q)(Product_{k>0} (1+q^(2k-1)))^24 = 64(G_n)^24 where q=e^(-pi sqrt(n)) and G_n is Ramanujan's class invariant.
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PROGRAM
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(PARI) a(n)=local(A); if(n<-1, 0, n++; A=x^n*O(x); polcoeff( (eta(x^2+A)^2/eta(x+A)/eta(x^4+A))^24, n))
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CROSSREFS
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Cf. A007191(n)=-(-1)^n*a(n).
Sequence in context: A045854 A014809 A007191 this_sequence A001496 A055754 A035707
Adjacent sequences: A097337 A097338 A097339 this_sequence A097341 A097342 A097343
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 05 2004
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