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Search: id:A078906
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| A078906 |
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Expansion of j in powers of Gamma(5)-modular function Lambda^5. |
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+0
3
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| 1, 739, 196874, 22478125, 1086128125, 35307387500, 913727546875, 20389341653125, 410010534950000, 7633186177665625, 133911227595521875, 2240979684247156250, 36090410657726350000, 563019001047724506250
(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 Eq. (5.3).
A. Erdelyi, Higher Transcendental Functions, McGraw-Hill, 1955, Vol. 3, p. 24.
H. McKean and V. Moll. Elliptic Curves, Camb. Univ. Press, p. 22.
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FORMULA
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G.f.: (1+228x+494x^2-228x^3+x^4)^3/(x(1-11x-x^2)^5).
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EXAMPLE
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j = 1/x + 739 + 196874*x + 22478125*x^2 + ... where x=Lambda^5=A078905.
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MAPLE
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t1:=1+228*z+494*z^2-228*z^3+z^4; t2:=-t1^3/(z*(z^2+11*z-1)^5); # t2 is Duke's g.f.
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PROGRAM
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(PARI) a(n)=polcoeff((1-228*(x^3-x)+494*x^2+x^4)^3/x/(1-11*x-x^2)^5+x*O(x^n), n)
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CROSSREFS
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Cf. A078905, A000521. A066404(n)=(-1)^n*a(n-1).
Sequence in context: A004078 A043633 A077723 this_sequence A066404 A066402 A119264
Adjacent sequences: A078903 A078904 A078905 this_sequence A078907 A078908 A078909
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KEYWORD
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nonn,easy
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AUTHOR
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Michael Somos, Dec 12 2002
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