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Search: id:A128128
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| A128128 |
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Expansion of chi(-q^3)/ chi^3(-q) in powers of q where chi() is a Ramanujan theta function. |
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5
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| 1, 3, 6, 12, 21, 36, 60, 96, 150, 228, 342, 504, 732, 1050, 1488, 2088, 2901, 3996, 5460, 7404, 9972, 13344, 17748, 23472, 30876, 40413, 52644, 68268, 88152, 113364, 145224, 185352, 235734, 298800, 377514, 475488, 597108, 747690, 933672, 1162824
(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^2)^3* eta(q^3)/ (eta(q)^3* eta(q^6)) in powers of q.
Euler transform of period 6 sequence [ 3, 0, 2, 0, 3, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)=u^2 +v -2*u*v^2.
G.f. A(x) satisfies 0=f(A(x), A(x^3)) where f(u, v)=(u+u^2+u^3) -v^3*(1-2*u+4*u^2).
G.f. A(x) satisfies 0=f(A(x), A(x^5)) where f(u, v)=u^6 +v^6 -16*u^5*v^5 +20*u^4*v^4 +10*u^2*v^2*(u^3+v^3) -20*u^3*v^3 -5*u*v*(u^3+v^3) +5*u^2*v^2 -u*v.
Expansion of b(q^2)/b(q) in powers of q where b() is a cubic AGM analog function.
G.f. is a period 1 Fourier series which satisfies f(-1/ (18 t)) = (1/2) g(t) where q = exp(2 pi i t) and g() is g.f. for A062242.
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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^2+A)^3/ eta(x+A)^3* eta(x^3+A)/ eta(x^6+A), n))}
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CROSSREFS
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a(n)=3*A128129(n) if n>0.
Sequence in context: A034344 A054578 A115855 this_sequence A006330 A087503 A133627
Adjacent sequences: A128125 A128126 A128127 this_sequence A128129 A128130 A128131
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Feb 15 2007
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