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Search: id:A138521
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| A138521 |
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Expansion of chi(-q)^5 / chi(-q^5) in powers of q where chi() is a Ramanujan theta function. |
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+0
2
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| 1, -5, 10, -15, 30, -55, 80, -120, 190, -285, 410, -585, 840, -1190, 1640, -2240, 3070, -4170, 5570, -7400, 9830, -12960, 16920, -21990, 28520, -36805, 47180, -60225, 76720, -97350, 122880, -154610, 194110, -242880, 302740, -376295, 466710, -577270, 711800, -875520
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of (eta(q) / eta(q^2))^5 * eta(q^10) / eta(q^5) in powers of q.
Euler transform of period 10 sequence [ -5, 0, -5, 0, -4, 0, -5, 0, -5, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = v * ((u+1)^2 + v) - (v + 4 * u).
G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u - v)^4 - u * v * (u - 1) * (u + 4) * (v - 1) * (v + 4).
G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = 4 g(t) where q = exp(2 pi i t) and g() is g.f. for A095813.
G.f.: Product_{k>0} (1 + x^(5*k)) / (1 + x^k)^5.
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EXAMPLE
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1 - 5*q + 10*q^2 - 15*q^3 + 30*q^4 - 55*q^5 + 80*q^6 - 120*q^7 + 190*q^8 + ...
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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 + A) / eta(x^2 + A) )^5 * eta(x^10 + A) / eta(x^5 + A), n))}
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CROSSREFS
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Cf. -5 * A138519(n) = a(n) unless n=0. Convolution inverse of A132985.
Sequence in context: A008439 A031471 A045206 this_sequence A022600 A067237 A048703
Adjacent sequences: A138518 A138519 A138520 this_sequence A138522 A138523 A138524
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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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