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Search: id:A138522
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| A138522 |
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Expansion of (eta(q^2) / eta(q^5))^3 * eta(q^10) / eta(q) in powers of q. |
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3
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| 1, 1, -1, 0, -1, 1, 4, -4, -1, -3, 3, 12, -12, -2, -8, 8, 31, -30, -5, -20, 19, 72, -68, -12, -44, 41, 154, -144, -24, -90, 84, 312, -289, -48, -178, 164, 603, -554, -92, -336, 307, 1122, -1024, -168, -612, 557, 2024, -1836, -300, -1087, 983, 3552, -3206, -522, -1880, 1692, 6088, -5472, -886, -3180, 2852
(list; graph; listen)
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OFFSET
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0,7
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FORMULA
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Euler transform of period 10 sequence [ 1, -2, 1, -2, 4, -2, 1, -2, 1, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u - v)^2 - u * (u + 4) * (1 - v).
G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u-v)^4 - u * (1 - u) * (4 + u) * v * (1 - v) * (4 + v).
G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = (5/4) / f(t) where q = exp(2 pi i t).
G.f.: Product_{k>0} (1 + x^k)^4 * P(10, x^k) / P(5, x^k)^2 where P(n, x) is the n-th cyclotomic polynomial.
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EXAMPLE
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1 + q - q^2 - q^4 + q^5 + 4*q^6 - 4*q^7 - q^8 - 3*q^9 + 3*q^10 + 12*q^11 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^10 + A) / eta(x + A) * ( eta(x^2 + A) / eta(x^5 + A) )^3, n))}
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CROSSREFS
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A095813(n) = a(n) unless n=0. Convolution inverse of A138520.
Sequence in context: A094884 A053216 A095813 this_sequence A010656 A023401 A055180
Adjacent sequences: A138519 A138520 A138521 this_sequence A138523 A138524 A138525
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Mar 23 2008
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