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Coefficients in expansion of 691*E_12/Delta where Delta is the generating function of Ramanujan's tau function (A000594).
2

%I #43 Apr 09 2018 07:40:05

%S 691,82104,136046844,14852188160,597231279270,13989886672896,

%T 230243024654600,2938148100366336,30857982903707085,

%U 277430202679296000,2194920198781034220,15594068776929177600,101032430846167832154,604150780302870773760

%N Coefficients in expansion of 691*E_12/Delta where Delta is the generating function of Ramanujan's tau function (A000594).

%H Seiichi Manyama, <a href="/A288837/b288837.txt">Table of n, a(n) for n = -1..1000</a>

%F a(n) = 691*A000521(n) = 691*A289063(n+1) for n > 0.

%F G.f.: 691*j - 432000 where j is the elliptic modular invariant.

%F a(n) ~ 691 * exp(4*Pi*sqrt(n)) / (sqrt(2) * n^(3/4)). - _Vaclav Kotesovec_, Apr 09 2018

%t terms = 14;

%t E12[x_] = 1 + (65520/691)*Sum[k^11*x^k/(1 - x^k), {k, 1, terms}];

%t 691*E12[x]/QPochhammer[x]^24 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)

%Y Cf. A035230, A035281, A035293, A035314, A035315.

%Y Cf. A000521 (j), A000594 (Delta), A029828 (691*E_12), A289063 (q*E_6^2/Delta), A289981.

%K nonn

%O -1,1

%A _Seiichi Manyama_, Jul 17 2017