OFFSET
0,3
FORMULA
a(n) ~ r^(1/8) * (log(r)^2 + 8*polylog(2, 1-r)) * exp(sqrt(2*(log(r)^2 + 8*polylog(2, 1-r))*n)) / (2^(7/2) * Pi^2 * sqrt(1 + 3*r) * n^(3/2)), where r = 0.2755080409994... is the smallest real root of the equation r = (1-r)^4.
MATHEMATICA
nmax = 40; CoefficientList[Series[Sum[x^(k*(k+1)/2)/Product[1-x^j, {j, 1, k}]^4, {k, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 02 2024
STATUS
approved