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Search: id:A108481
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| A108481 |
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Expansion of a Hauptmodul for Gamma_1(7). |
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+0
1
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| 1, 3, 4, 3, 0, -5, -7, -2, 8, 16, 12, -7, -29, -35, -10, 37, 70, 53, -21, -106, -126, -38, 119, 226, 164, -70, -326, -378, -106, 353, 652, 469, -189, -885, -1015, -290, 910, 1664, 1179, -483, -2205, -2492, -692, 2212, 3998, 2809, -1120, -5119, -5754, -1598, 4992, 8968, 6251, -2506, -11285, -12579
(list; graph; listen)
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OFFSET
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-1,2
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REFERENCES
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W. Duke, Continued fractions and modular functions, Bull. Amer. Math. Soc. 42 (2005), 137-162. See page 156.
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FORMULA
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G.f.: (1/x)Product_{k>0} (1-x^(7k-2))^2(1-x^(7k-5))^2(1-x^(7k-3))(1-x^(7k-4))/((1-x^(7k-1))(1-x^(7k-6)))^3.
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)= +v -w +u^2 -2*w*v -3*u*w +4*u*v +w^2*v +u*w^2 -u^2*v -u^2*w^2 +4*u^2*w -4*u^2*w*v -5*u*v^2 +5*u*w*v^2.
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PROGRAM
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(PARI) {a(n)=if(n<-1, 0, n++; polcoeff( prod(k=1, n, (1-x^k+x*O(x^n))^[0, -3, 2, 1, 1, 2, -3][k%7+1]), n))}
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CROSSREFS
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Sequence in context: A059114 A072681 A064460 this_sequence A078070 A111028 A096646
Adjacent sequences: A108478 A108479 A108480 this_sequence A108482 A108483 A108484
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jun 04 2005
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