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Search: id:A132180
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| A132180 |
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Expansion of eta(q^3)^3/( eta(q)* eta(q^2)* eta(q^6)) in powers of q. |
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2
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| 1, 1, 3, 1, 6, 3, 12, 5, 21, 10, 36, 15, 60, 26, 96, 39, 150, 63, 228, 92, 342, 140, 504, 201, 732, 295, 1050, 415, 1488, 591, 2088, 818, 2901, 1140, 3996, 1554, 5460, 2126, 7404, 2861, 9972, 3855, 13344, 5126, 17748, 6816, 23472, 8970, 30876, 11793, 40413
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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Euler transform of period 6 sequence [ 1, 2, -2, 2, 1, 0, ...].
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (v^2- 2*u)^3 -u^4* (2*u -3*v^2)* (4*u -3*v^2).
G.f. is a period 1 Fourier series which satisfies f(-1/ (6 t)) = (2/3) g(t) where q = exp(2 pi i t) and g() is g.f. for A132179.
G.f.: Product_{k>0} (1+x^k+x^(2*k))^2/( (1+x^k)^2* (1-x^k+x^(2*k))).
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EXAMPLE
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1 + q + 3*q^2 + q^3 + 6*q^4 + 3*q^5 + 12*q^6 + 5*q^7 + 21*q^8 + 10*q^9 + ...
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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^3+A)^3/ eta(x+A)/ eta(x^2+A)/ eta(x^6+A), n))}
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CROSSREFS
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A128128(n) = a(2*n). A132302(n) = a(2*n+1).
Adjacent sequences: A132177 A132178 A132179 this_sequence A132181 A132182 A132183
Sequence in context: A107884 A121443 A008795 this_sequence A126191 A070883 A120029
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 12 2007
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