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Search: id:A121589
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| A121589 |
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Expansion of (eta(q^9)/eta(q))^3 in powers of q. |
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+0
1
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| 1, 3, 9, 22, 51, 108, 221, 429, 810, 1476, 2631, 4572, 7802, 13056, 21519, 34918, 55935, 88452, 138332, 213990, 327852, 497592, 748833, 1117692, 1655719, 2434938, 3556791, 5161808, 7445631, 10677096, 15226658, 21599469, 30485268, 42817788
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OFFSET
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1,2
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FORMULA
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Euler transform of period 9 sequence [ 3, 3, 3, 3, 3, 3, 3, 3, 0, ...].
G.f.: x*(Product_{k>0} (1-x^(9n))/(1-x^n))^3.
Expansion of c(q^3) / (3 * b(q)) in powers of q where b(), c() are cubic AGM functions.
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u - v^2) * (u^2 - v) - 2 * u * v * ( 3 * (u + v) + 13 * u * v ).
G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = u^3 - v * (1 + 9 * v + 27 * v^2) * (1 + 9 * u + 27 * 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) = u1 * u2 - (1 + 3 * (u1 + u2)) * (u3 + u6 + 9 * u3 * u6).
G.f. is a period 1 Fourier series which satisfies f(-1 / (9 t)) = (1/27) / f(t) where q = exp(2 pi i t).
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EXAMPLE
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q + 3*q^2 + 9*q^3 + 22*q^4 + 51*q^5 + 108*q^6 + 221*q^7 + 429*q^8 + ...
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PROGRAM
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(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( (eta(x^9+A)/eta(x+A))^3, n))}
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CROSSREFS
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Sequence in context: A034505 A143099 A000711 this_sequence A000716 A001628 A099166
Adjacent sequences: A121586 A121587 A121588 this_sequence A121590 A121591 A121592
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 09 2006
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