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Search: id:A133099
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| A133099 |
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Expansion of ( eta(q) / eta(q^13) )^2 in powers of q. |
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+0
2
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| 1, -2, -1, 2, 1, 2, -2, 0, -2, -2, 1, 0, 0, 4, -1, -4, 6, 2, 4, -6, -2, -4, -4, 0, -1, 0, 11, -2, -11, 16, 6, 12, -14, -2, -12, -12, 3, -2, -2, 24, -5, -24, 34, 12, 25, -32, -6, -24, -22, 4, -3, -2, 51, -10, -50, 72, 27, 52, -64, -12, -50, -48, 10, -8, -4, 98, -20, -96, 136, 48, 96, -120, -24, -90, -86, 16, -14, -8, 184, -36, -176, 252
(list; graph; listen)
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OFFSET
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-1,2
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FORMULA
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Euler transform of period 13 sequence [ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^3 + v^3 - 13*u*v - 4*u*v * (u+v) - (u*v)^2.
G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u^2 - u*v + v^2)^2 - u*v * (13 + 6*u + u^2) * (13 + 6*v + v^2).
G.f. is a period 1 Fourier series which satisfies f(-1 / (13 t)) = 13 / f(t) where q = exp(2 pi i t).
G.f.: x^(-1) * ( Product_{k>0} (1 - x^k) / (1 - x^(13*k)) )^2.
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EXAMPLE
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1/q - 2 - q + 2*q^2 + q^3 + 2*q^4 - 2*q^5 - 2*q^7 - 2*q^8 + q^9 + ...
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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^13 + A))^2, n))}
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CROSSREFS
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A058496(n) = a(n) unless n=0. Convolution inverse of A121597.
Sequence in context: A063279 A124333 A002107 this_sequence A006571 A094781 A023582
Adjacent sequences: A133096 A133097 A133098 this_sequence A133100 A133101 A133102
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Sep 11 2007
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