A078906 Expansion of j in powers of Gamma(5)-modular function Lambda^5.

1, 739, 196874, 22478125, 1086128125, 35307387500, 913727546875, 20389341653125, 410010534950000, 7633186177665625, 133911227595521875, 2240979684247156250, 36090410657726350000, 563019001047724506250

Offset

-1,2

References

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.

Links

Table of n, a(n) for n=-1..12.

Formula

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

Example

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

Maple

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.

Prog

(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)

Crossrefs

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

Sequence in context: A077723 A235466 A202417 * A066404 A066402 A243778

Adjacent sequences: A078903 A078904 A078905 * A078907 A078908 A078909

Keyword

nonn,easy

Author

Michael Somos, Dec 12 2002

Status

approved