|
|
A261384
|
|
Expansion of Product_{k>=1} (1+x^k)^(2*k-1) / (1-x^k)^(2*k).
|
|
3
|
|
|
1, 3, 12, 39, 117, 331, 893, 2307, 5766, 13986, 33046, 76302, 172567, 383013, 835731, 1795236, 3801105, 7941439, 16386777, 33423342, 67435311, 134675784, 266385932, 522135379, 1014643823, 1955656848, 3740191268, 7100290646, 13383997996, 25058666367
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ (7*Zeta(3))^(2/9) * exp(1/6 - Pi^4/(6048*Zeta(3)) - Pi^2 * n^(1/3) / (12*(7*Zeta(3))^(1/3)) + 3/2*(7*Zeta(3))^(1/3) * n^(2/3)) / (A^2 * 2^(1/6) * sqrt(3*Pi) * n^(13/18)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant.
|
|
MATHEMATICA
|
nmax = 40; CoefficientList[Series[Product[(1+x^k)^(2*k-1)/(1-x^k)^(2*k), {k, 1, nmax}], {x, 0, nmax}], x]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|