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Search: id:A111580
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| A111580 |
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Expansion of eta(q)^2*eta(q^2)*eta(q^10)^3/eta(q^5)^2 in powers of q. |
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+0
2
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| 1, -2, -2, 4, 1, 4, -6, -8, 7, -2, 12, -8, -12, 12, -2, 16, -16, -14, 20, 4, 12, -24, -22, 16, 1, 24, -20, -24, 30, 4, 32, -32, -24, 32, -6, 28, -36, -40, 24, -8, 42, -24, -42, 48, 7, 44, -46, -32, 43, -2, 32, -48, -52, 40, 12, 48, -40, -60, 60, -8, 62, -64, -42, 64, -12, 48, -66, -64, 44, 12, 72, -56, -72, 72
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 249 Entry 8(i).
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FORMULA
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Euler transform of period 10 sequence [ -2, -3, -2, -3, 0, -3, -2, -3, -2, -4, ...].
G.f.: Sum_{k>0} kronecker(k, 5)*k*x^k/(1-x^(2k)) = x Product_{k>0} (1-x^k)^2*(1-x^(2k))*(1+x^(5k))^2*(1-x^(10k)).
a(2*n) = -2*a(n).
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, (n/d%2)*d*kronecker(d, 5)))
(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x+A)^2*eta(x^2+A)*eta(x^10+A)^3/eta(x^5+A)^2, n))}
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CROSSREFS
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Sequence in context: A023137 A065273 A140819 this_sequence A138558 A066202 A027420
Adjacent sequences: A111577 A111578 A111579 this_sequence A111581 A111582 A111583
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Aug 08 2005
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