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Search: id:A131796
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| A131796 |
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Expansion of chi(-q^3)^2*chi(-q^5)^2/(chi(-q)*chi(-q^15)) in powers of q where chi() is a Ramanujan theta function. |
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+0
3
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| 1, 1, 1, 0, 0, -1, -1, 0, 1, 0, -1, 0, 0, 1, 2, 1, -2, -3, -1, 1, 2, 3, 0, -3, -1, 2, 2, 0, -2, -6, -3, 4, 7, 3, -2, -5, -6, 2, 8, 3, -5, -6, -2, 4, 12, 7, -10, -15, -6, 5, 13, 12, -4, -18, -7, 11, 14, 6, -10, -24, -14, 20, 32, 12, -12, -29, -24, 9, 36, 15, -22, -30, -13, 22, 50, 27, -36, -63, -26, 24, 56, 45, -22, -69, -30, 42, 62
(list; graph; listen)
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OFFSET
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0,15
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FORMULA
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Euler transform of period 30 sequence [ 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= v^2 +u*(2 -4*v +u*v).
G.f.: Product_{k>0} (1+x^k)* (1+x^(15*k))/ ((1+x^(3*k))* (1+x^(5*k)))^2.
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^30+A)/eta(x+A)/eta(x^15+A)* (eta(x^3+A)*eta(x^5+A)/eta(x^6+A)/eta(x^10+A))^2, n))}
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CROSSREFS
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Cf. A131794(n)= a(n) unless n=0. A131797(n)= -a(n) unless n=0.
Sequence in context: A124448 A143343 A138243 this_sequence A131797 A145727 A145782
Adjacent sequences: A131793 A131794 A131795 this_sequence A131797 A131798 A131799
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jul 16 2006
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