OFFSET
0,10
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ r^2 * (7*log(r)^2 + polylog(2, r^2))^(1/4) * exp(2*sqrt((7*log(r)^2 + polylog(2, r^2))*n)) / (2*sqrt(7*Pi*(7 - 5*r^2)) * n^(3/4)), where r = 0.839833147032421662... is the positive real root of the equation r^2 = 1 - r^7.
MATHEMATICA
nmax = 100; CoefficientList[Series[Sum[x^(7*k^2)/Product[1-x^j, {j, 1, 7*k-1}], {k, 1, Sqrt[nmax/7]}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 15 2024
STATUS
approved