|
|
A285048
|
|
Expansion of Product_{k>=0} 1/(1-x^(4*k+1))^(4*k+1).
|
|
4
|
|
|
1, 1, 1, 1, 1, 6, 6, 6, 6, 15, 30, 30, 30, 43, 88, 123, 123, 140, 250, 385, 455, 476, 678, 1098, 1413, 1564, 1913, 2918, 4048, 4707, 5452, 7572, 10747, 13265, 15195, 19534, 27349, 35146, 41042, 50011, 67596, 88897, 106519, 126635, 164230, 216862, 266473, 314883
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ 4 * Pi * 2^(25/72) * Zeta(3)^(11/72) * exp(4*c + 3 * 2^(-4/3) * Zeta(3)^(1/3) * n^(2/3)) / (sqrt(3) * Gamma(1/4)^3 * n^(47/72)), where c = Integral_{x=0..inf} ((-19/(exp(x)*96) + 1/(exp(x)*(1 - exp(-4*x))^2) - 1/(16*x^2) - 3/(16*x))/x) dx = 0.09601010361866957956805888476415949391295401812706635... - Vaclav Kotesovec, Apr 16 2017
|
|
MATHEMATICA
|
nmax = 50; CoefficientList[Series[Product[1/(1-x^(4*k-3))^(4*k-3), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 16 2017 *)
|
|
CROSSREFS
|
Product_{k>=0} 1/(1-x^(m*k+1))^(m*k+1): A262811 (m=2), A262947 (m=3), this sequence (m=4), A285049 (m=5).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|