A037945 - OEIS

%I #33 Feb 27 2018 10:53:05

%S 1,456,50652,-316352,-2377410,23097312,-16917544,-383331840,

%T 1403363637,-1084098960,-16212108,-16023861504,50421615062,

%U -7714400064,-120420571320,-8939761664,225070099506,639933818472

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

%H Seiichi Manyama, <a href="/A037945/b037945.txt">Table of n, a(n) for n = 1..1000</a>

%H 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 S. C. Milne, <a href="https://arxiv.org/abs/math/0009130">Hankel determinants of Eisenstein series</a>, preprint, arXiv:0009130 [math.NT], 2000.

%H <a href="/index/Gre#groups_modular">Index entries for sequences related to modular groups</a>

%F a(n) == A013967(n) mod 174611. - _Seiichi Manyama_, Feb 02 2017

%F G.f.: (E_4(q)^3 - E_6(q)^2)/12^3 * E_4(q)^2. - _Seiichi Manyama_, Jun 09 2017

%F G.f.: 691/(1728*441) * (E_8(q)*E_12(q) - E_10(q)^2). - _Seiichi Manyama_, Jul 25 2017

%e q^2 + 456*q^4 + ...

%t terms = 18;

%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms+1}];

%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms+1}];

%t ((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 Cf. A013967, A290180.

%K sign

%O 1,2

%A _N. J. A. Sloane_