Search: id:A078906
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%I A078906
%S A078906 1,739,196874,22478125,1086128125,35307387500,913727546875,
%T A078906 20389341653125,410010534950000,7633186177665625,133911227595521875,
%U A078906 2240979684247156250,36090410657726350000,563019001047724506250
%N A078906 Expansion of j in powers of Gamma(5)-modular function Lambda^5.
%D A078906 W. Duke, Continued fractions and modular functions, Bull. Amer. Math. 
               Soc., 42 (2005), 137-162; see Eq. (5.3).
%D A078906 A. Erdelyi, Higher Transcendental Functions, McGraw-Hill, 1955, Vol. 
               3, p. 24.
%D A078906 H. McKean and V. Moll. Elliptic Curves, Camb. Univ. Press, p. 22.
%F A078906 G.f.: (1+228x+494x^2-228x^3+x^4)^3/(x(1-11x-x^2)^5).
%e A078906 j = 1/x + 739 + 196874*x + 22478125*x^2 + ... where x=Lambda^5=A078905.
%p A078906 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.
%o A078906 (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)
%Y A078906 Cf. A078905, A000521. A066404(n)=(-1)^n*a(n-1).
%Y A078906 Sequence in context: A004078 A043633 A077723 this_sequence A066404 A066402 
               A119264
%Y A078906 Adjacent sequences: A078903 A078904 A078905 this_sequence A078907 A078908 
               A078909
%K A078906 nonn,easy
%O A078906 -1,2
%A A078906 Michael Somos, Dec 12 2002

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