%I #5 Apr 30 2014 01:38:50

%S 1,739,196874,22478125,1086128125,35307387500,913727546875,

%T 20389341653125,410010534950000,7633186177665625,133911227595521875,

%U 2240979684247156250,36090410657726350000,563019001047724506250

%N Expansion of j in powers of Gamma(5)-modular function Lambda^5.

%D W. Duke, Continued fractions and modular functions, Bull. Amer. Math. Soc., 42 (2005), 137-162; see Eq. (5.3).

%D A. Erdelyi, Higher Transcendental Functions, McGraw-Hill, 1955, Vol. 3, p. 24.

%D H. McKean and V. Moll. Elliptic Curves, Camb. Univ. Press, p. 22.

%F G.f.: (1+228x+494x^2-228x^3+x^4)^3/(x(1-11x-x^2)^5).

%e j = 1/x + 739 + 196874*x + 22478125*x^2 + ... where x=Lambda^5=A078905.

%p 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 (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 Cf. A078905, A000521. A066404(n)=(-1)^n*a(n-1).

%K nonn,easy

%O -1,2

%A _Michael Somos_, Dec 12 2002