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Expansion of modular function j/256 in powers of m=k^2=lambda(t).
1

%I #8 Jun 17 2017 03:04:37

%S 1,-1,3,0,3,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,

%T 24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,

%U 47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70

%N Expansion of modular function j/256 in powers of m=k^2=lambda(t).

%D J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 115.

%D A. Erdelyi, Higher Transcendental Functions, McGraw-Hill, 1955, Vol. 3, p. 22.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: (1-x+x^2)^3/(x-x^2)^2. a(n)=n, n>2.

%e j/256 = 1/m^2 -1/m +3 +0m +3m^2 +3m^3 +4m^4 +...

%o (PARI) a(n)=polcoeff((1-x+x^2)^3/(x-x^2)^2+x*O(x^n),n)

%Y Cf. A000027, A000521.

%K sign,easy

%O -2,3

%A _Michael Somos_, Dec 12 2002