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%I #20 Aug 19 2018 10:37:03
%S 0,1,-24,196812,38262208,40310333070,16012430173152,10091293275887096,
%T 5000566664612497920,2783095702986935913957,1463183098457857467833520,
%U 790439623931093138858233092,421526637613212526260386954496,226162012708702132169932739559302,120998755205524059896241960291393216
%N Coefficients of expansion of Phi(tau) = E_2*E_4/(E_6*j).
%H Seiichi Manyama, <a href="/A145200/b145200.txt">Table of n, a(n) for n = 0..367</a>
%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
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EisensteinSeries.html">Eisenstein Series.</a>
%F a(n) ~ 2 * Pi^5 * exp(2*Pi*n) / (27 * Gamma(1/4)^8). - _Vaclav Kotesovec_, Apr 07 2018
%e G.f. = q - 24*q^2 + 196812*q^3 + 38262208*q^4 + 40310333070*q^5 + 16012430173152*q^6 + ...
%t a[ n_] := SeriesCoefficient[ (1 - 24 Sum[ DivisorSigma[ 1, k] x^k, {k, n}]) (1 + 240 Sum[ DivisorSigma[ 3, k] x^k, {k, n}]) / ((1 - 504 Sum[ DivisorSigma[ 5, k] x^k, {k, n}]) KleinInvariantJ[ Log[x] / (2 Pi I)] 1728), {x, 0, n}]; (* _Michael Somos_, Jan 15 2015 *)
%Y Cf. A000521 (j), A006352 (E_2), A004009 (E_4), A013973 (E_6), A030185.
%K sign
%O 0,3
%A _N. J. A. Sloane_, Feb 28 2009
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