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Search: id:A115784
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| A115784 |
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Expansion of b(q)/a(q) in powers of q of cubic AGM analogue. |
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+0
1
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| 1, -9, 54, -324, 1989, -12204, 74844, -459072, 2815830, -17271468, 105938118, -649793448, 3985642908, -24446767374, 149949318096, -919745243064, 5641448209173, -34602992662356, 212244632371188, -1301846473509156
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(q)=g.f. A004016, b(q)=g.f. A005928.
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REFERENCES
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J. M. Borwein, P. B. Borwein and F. Garvan, Some Cubic Modular Identities of Ramanujan, Trans. Amer. Math. Soc. 343 (1994), 35-47
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FORMULA
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Expansion of eta(q)^3/(eta(q)^3+9*eta(q^9)^3) in powers of q.
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)=(1-u*v)^3-(1-u^3)*(1-v^3).
G.f. A(x) satisfies 0=f(A(x), A(x^3)) where f(u, v)=(1+2*u)^3*v^3 -9*u*(1+u+u^2).
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)=(1+2*u1)*(1+2*u2)*u3*u6 -3*(u1+u2+u1*u2).
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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)^3/(eta(x+A)^3+9*x*eta(x^9+A)^3), n))}
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CROSSREFS
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Sequence in context: A001392 A079764 A079761 this_sequence A037599 A037704 A093847
Adjacent sequences: A115781 A115782 A115783 this_sequence A115785 A115786 A115787
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jan 31 2006
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