|
|
A258341
|
|
Expansion of Product_{k>=1} (1+x^k)^(k*(k+1)).
|
|
9
|
|
|
1, 2, 7, 24, 65, 184, 487, 1254, 3145, 7706, 18480, 43490, 100692, 229472, 515802, 1144416, 2508948, 5439642, 11671859, 24801738, 52221911, 109013538, 225718717, 463769652, 945915199, 1915895576, 3854803572, 7706786958, 15314564282, 30255672820, 59440488874
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ 7^(1/8) / (2^(47/24) * 15^(1/8) * n^(5/8)) * exp(2025*Zeta(3)^3 / (49*Pi^8) - 135*(15/14)^(1/4) * Zeta(3)^2 / (14*Pi^5) * n^(1/4) + 3*sqrt(15/14) * Zeta(3) / Pi^2 * sqrt(n) + 2*(14/15)^(1/4)*Pi/3 * n^(3/4)), where Zeta(3) = A002117.
|
|
MATHEMATICA
|
nmax=30; CoefficientList[Series[Product[(1+x^k)^(k*(k+1)), {k, 1, nmax}], {x, 0, nmax}], x]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|