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A145727
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Expansion of f(q) * f(q^15) / (f(-q^6) * f(-q^10)) in powers of q where f() is a Ramanujan theta function.
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2
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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; refs; listen; history; internal format)
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OFFSET
| 0,15
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| Expansion of (eta(q^2) * eta(q^30))^3 / (eta(q) * eta(q^4) * eta(q^6) * eta(q^10) * eta(q^15) * eta(q^60)) in powers of q.
Euler transform of period 60 sequence.
G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = f(t) where q = exp(2 pi i t).
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EXAMPLE
| 1 + q - q^2 - q^5 + q^6 - q^8 + q^10 + q^13 - 2*q^14 + q^15 + 2*q^16 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^30 + A))^3 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^10 + A) * eta(x^15 + A) * eta(x^60 + A)), n))}
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CROSSREFS
| Convolution inverse of A094023. A145726(n) = a(n) unless n=0.
Sequence in context: A131796 A131797 * A145782 A131794 A145726 A181631
Adjacent sequences: A145724 A145725 A145726 * A145728 A145729 A145730
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Oct 23 2008
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