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a(n) = numerator of Atkin polynomials A_n(j) evaluated at j = 1728.
1

%I #4 Sep 25 2017 07:14:51

%S 1008,421344,901254816,77507914176,33392993024160,14400272882673216,

%T 80771130598914068544,13408007679419735378304,

%U 19679603271468316601505696,8496755026505881957246582080,215817577673249401714063184832,93197366130882174446119601563776,1006205363432069396407530278283307584

%N a(n) = numerator of Atkin polynomials A_n(j) evaluated at j = 1728.

%H M. Kaneko and D. Zagier, <a href="http://www2.math.kyushu-u.ac.jp/~mkaneko/papers/atkin.pdf">Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials</a>, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998

%F See Maple code for formula.

%e 1008, 421344, 901254816/5, 77507914176, 33392993024160, 14400272882673216, 80771130598914068544/13, ...

%p af:=proc(a,n) mul(a+i,i=0..n-1); end; A1728:=n->-12^(3*n+1)*af(-1/12,n)*af(7/12,n)/(2*n-1)!;

%Y Cf. A145295, A145093.

%K nonn,frac

%O 1,1

%A _N. J. A. Sloane_, Feb 28 2009