|
|
A299953
|
|
Coefficients in expansion of (E_4^3/E_6^2)^(1/12).
|
|
19
|
|
|
1, 144, 27648, 12540096, 4971036672, 2263040955360, 1031452724072448, 487587831652591488, 233267529030162186240, 113311495859272029716688, 55566291037565862262794240, 27487705978359515260636550208, 13689979692617556597746930024448
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ 2^(2/3) * sqrt(Pi) * exp(2*Pi*n) / (3^(1/12) * Gamma(1/6) * Gamma(1/4)^(2/3) * n^(5/6)). - Vaclav Kotesovec, Mar 04 2018
|
|
MATHEMATICA
|
terms = 13;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
|
|
CROSSREFS
|
(E_4^3/E_6^2)^(k/288): A289365 (k=1), A299694 (k=2), A299696 (k=3), A299697 (k=4), A299698 (k=6), A299943 (k=8), A299949 (k=9), A289369 (k=12), A299950 (k=16), A299951 (k=18), this sequence (k=24), A299993 (k=32), A299994 (k=36), A300052 (k=48), A300053 (k=72), A300054 (k=96), A300055 (k=144), A289209 (k=288).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|