OFFSET
0,2
FORMULA
a(n) ~ 2^(2*n - 1/3) * exp(3*n^(1/3)/2^(2/3) - 1 + c) / (sqrt(3*Pi) * n^(5/6)), where c = Sum_{k>=2} (-1)^k * (1 - 1/sqrt(1 - 4^(1-k)))/k = -0.0680700790487788003241709878640131435678833005035785286095068...
MATHEMATICA
nmax = 25; CoefficientList[Series[Product[(1 + x^k)^Binomial[2 k, k], {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 25; CoefficientList[Series[Exp[Sum[-(-1)^j * (1/Sqrt[1 - 4*x^j] - 1)/j, {j, 1, nmax}]], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 10 2021
STATUS
approved