A299954 - OEIS

%I #23 Apr 09 2018 07:47:07

%S 1,-120,10260,-901120,91676610,-10868097024,1455225319640,

%T -213263515975680,33415165837622655,-5507368816607232000,

%U 944071154093581913700,-166969055816397343457280,30289678318291920442724670,-5611505834651089642200760320

%N Coefficients in expansion of 432 * (j^(1/2) + (j - 1728)^(1/2)) / (j^(1/2) - (j - 1728)^(1/2)), where j is the j-function.

%H Seiichi Manyama, <a href="/A299954/b299954.txt">Table of n, a(n) for n = -1..425</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Sato_series#Level_1">Ramanujan-Sato series</a>.

%F G.f.: 432 * (1 + (1 - 1728/j)^(1/2)) / (1 - (1 - 1728/j)^(1/2)).

%F G.f.: 432 * (E_4^(3/2) + E_6) / (E_4^(3/2) - E_6).

%F a(n) ~ -(-1)^n * 81 * Gamma(1/3)^9 * exp(Pi*sqrt(3)*n) / (2^(3/2) * Pi^(13/2) * n^(5/2)). - _Vaclav Kotesovec_, Apr 09 2018

%e G.f.: 1/q - 120 + 10260*q - 901120*q^2 + 91676610*q^3 - 10868097024*q^4 + ...

%Y Cf. A000521, A004009 (E_4), A013973 (E_6), A299413, A299955 (E_4^(3/2)).

%K sign

%O -1,2

%A _Seiichi Manyama_, Feb 22 2018