OFFSET
0,3
FORMULA
a(n) ~ (log(r)^2 + 3*polylog(2, 1-r))^(3/4) * exp(2*sqrt((log(r)^2 + 3*polylog(2, 1-r))*n)) / (4 * Pi^(3/2) * r^(2/3) * sqrt(2+r) * n^(5/4)), where r = 1 - A357471 = 0.4301597090019467340886... is the real root of the equation r^2 = (1-r)^3.
MATHEMATICA
nmax = 40; CoefficientList[Series[Sum[x^(k^2)/Product[1-x^j, {j, 1, k}]^3, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 02 2024
STATUS
approved