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A037945 Coefficients of unique normalized cusp form Delta_20 of weight 20 for full modular group.

%I A037945 #33 Feb 27 2018 10:53:05
%S A037945 1,456,50652,-316352,-2377410,23097312,-16917544,-383331840,
%T A037945 1403363637,-1084098960,-16212108,-16023861504,50421615062,
%U A037945 -7714400064,-120420571320,-8939761664,225070099506,639933818472
%N A037945 Coefficients of unique normalized cusp form Delta_20 of weight 20 for full modular group.
%H A037945 Seiichi Manyama, <a href="/A037945/b037945.txt">Table of n, a(n) for n = 1..1000</a>
%H A037945 Fernando Q. Gouvêa, <a href="http://projecteuclid.org/euclid.em/1047920420">Non-ordinary primes: a story</a>, Experimental Mathematics, Volume 6, Issue 3 (1997), 195-205.
%H A037945 S. C. Milne, <a href="https://arxiv.org/abs/math/0009130">Hankel determinants of Eisenstein series</a>, preprint, arXiv:0009130 [math.NT], 2000.
%H A037945 <a href="/index/Gre#groups_modular">Index entries for sequences related to modular groups</a>
%F A037945 a(n) == A013967(n) mod 174611. - _Seiichi Manyama_, Feb 02 2017
%F A037945 G.f.: (E_4(q)^3 - E_6(q)^2)/12^3 * E_4(q)^2. - _Seiichi Manyama_, Jun 09 2017
%F A037945 G.f.: 691/(1728*441) * (E_8(q)*E_12(q) - E_10(q)^2). - _Seiichi Manyama_, Jul 25 2017
%e A037945 q^2 + 456*q^4 + ...
%t A037945 terms = 18;
%t A037945 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms+1}];
%t A037945 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms+1}];
%t A037945 ((E4[x]^3 - E6[x]^2)/12^3)*E4[x]^2 + O[x]^(terms+1) // CoefficientList[#, x]& // Rest (* _Jean-François Alcover_, Feb 27 2018, after _Seiichi Manyama_ *)
%Y A037945 Cf. A013967, A290180.
%K A037945 sign
%O A037945 1,2
%A A037945 _N. J. A. Sloane_