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Search: id:A132976
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| A132976 |
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Expansion of (1/q) * psi(-q) / psi(-q^9) in powers of q where psi() is a Ramanujan theta function. |
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2
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| 1, -1, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, -3, 0, 0, 1, 0, 0, 4, 0, 0, -4, 0, 0, 1, 0, 0, 4, 0, 0, -6, 0, 0, 1, 0, 0, 5, 0, 0, -8, 0, 0, 1, 0, 0, 8, 0, 0, -10, 0, 0, 2, 0, 0, 11, 0, 0, -14, 0, 0, 4, 0, 0, 14, 0, 0, -19, 0, 0, 4, 0, 0, 17, 0, 0, -24, 0, 0, 4, 0, 0, 23
(list; graph; listen)
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OFFSET
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-1,22
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FORMULA
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Expansion of eta(q) * eta(q^4) * eta(q^18) / (eta(q^2) * eta(q^9) * eta(q^36)) in powers of q.
Euler transform of period 36 sequence [ -1, 0, -1, -1, -1, 0, -1, -1, 0, 0, -1, -1, -1, 0, -1, -1, -1, 0, -1, -1, -1, 0, -1, -1, -1, 0, 0, -1, -1, 0, -1, -1, -1, 0, -1, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6) = u3 * u6 - (u1 + u2 + u1*u2) * (u3 + u6 + 3).
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = 3 / f(t) where q = exp(2 pi i t).
a(3*n+1) = 0. a(3*n) = 0 unless n=0.
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EXAMPLE
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1/q - 1 - q^2 + q^5 + q^8 - q^11 + q^17 - 2*q^20 + 2*q^26 - 3*q^29 + ...
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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^4 + A) * eta(x^18 + A) / ( eta(x^2 + A) * eta(x^9 + A) * eta(x^36 + A) ), n))}
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CROSSREFS
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A062244(n) = a(3*n-1). Convolution inverse of A132975.
Sequence in context: A126825 A045833 A117896 this_sequence A143840 A028649 A097798
Adjacent sequences: A132973 A132974 A132975 this_sequence A132977 A132978 A132979
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Sep 07 2007
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