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Search: id:A128637
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| A128637 |
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Expansion of 3* (b(q)^2/b(q^2))/ (c(q)^2/c(q^2)) in powers of q where b(), c() are cubic AGM analog functions. |
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3
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| 1, -8, 24, -24, -40, 144, -120, -192, 600, -456, -688, 2016, -1464, -2096, 5952, -4176, -5800, 15984, -10920, -14816, 39888, -26688, -35488, 93888, -61752, -80824, 210576, -136536, -176320, 453456, -290448, -370688, 942936, -597600, -755024, 1901952, -1194216
(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 (phi(-q)/ phi(-q^3))^4 in powers of q where phi() is a Ramanujan theta function.
Expansion of ((eta(q)/ eta(q^3))^2* (eta(q^6)/ eta(q^2)))^4 in powers of q.
Euler transform of period 6 sequence [ -8, -4, 0, -4, -8, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u* (1-v)* (9-v) -(u-v)^2.
G.f.: (Product_{k>0} (1-x^k+x^(2k))/ (1+x^k+x^(2k)) )^4.
G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u^2*v^2 +9*u*v -12*u*v^2 +30*v^2 -108*v +81)* u -v^3.
G.f. is a period 1 Fourier series which satisfies f(-1/ (6 t)) = 9 g(t) where q = exp(2 pi i t) and g() is g.f. for A128640.
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EXAMPLE
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1 - 8*q + 24*q^2 - 24*q^3 - 40*q^4 + 144*q^5 - 120*q^6 - 192*q^7 + ...
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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^3+A))^2* eta(x^6+A)/ eta(x^2+A))^4, n))}
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CROSSREFS
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-8*A123633(n) = a(n) unless n = 0. Convolution inverse of A128639.
Sequence in context: A036562 A088448 A005878 this_sequence A109272 A052349 A029607
Adjacent sequences: A128634 A128635 A128636 this_sequence A128638 A128639 A128640
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Mar 16 2007
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