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Search: id:A108483
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| A108483 |
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Expansion of a modular function for Gamma(7). |
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+0
1
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| 1, 1, 0, 0, 0, -1, 0, 1, 1, 0, -1, -1, -1, 0, 2, 2, 0, -1, -2, -2, 0, 3, 3, 0, -2, -3, -3, 0, 5, 5, 1, -3, -5, -5, 0, 7, 7, 1, -5, -8, -7, 1, 11, 12, 2, -7, -12, -11, 1, 15, 16, 3, -11, -18, -15, 2, 23, 24, 5, -15, -26, -22, 3, 31, 33, 7, -22, -37, -30, 5, 44, 47, 11, -30, -52, -42, 6, 59, 63, 15, -42, -72, -56, 10, 82, 88, 22
(list; graph; listen)
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OFFSET
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0,15
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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 157.
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FORMULA
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Given g.f. A(x), then B(x)=x^-2*A(x^7) satisfies 0=f(B(x), B(x^2)) where f(u, v)= v^3 -u^6 +3*u^4*v +u^7*v^3 +u^2*v^9 +u^8*v^6 -3*u^2*v^2 -2*u*v^6 -5*u^3*v^5 -u^5*v^4 -u^9*v^2 -u^4*v^8 -u^6*v^7.
G.f.: Product_{k>0} (1-x^(7k-2))(1-x^(7k-5))/((1-x^(7k-1))(1-x^(7k-6))).
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1, n, (1-x^k+x*O(x^n))^[0, -1, 1, 0, 0, 1, -1][k%7+1]), n))}
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CROSSREFS
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Sequence in context: A097951 A058643 A029368 this_sequence A101565 A029341 A079070
Adjacent sequences: A108480 A108481 A108482 this_sequence A108484 A108485 A108486
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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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