OFFSET
0,2
FORMULA
a(n)^(1/n) ~ (1+r)^(r*n/2 - 1/4) / ((2*Pi*n)^r * (1-r)^(r*n/2 + r - 1/4)), where r = 0.9222727963503830123185148157257918806196371551687495361664171679710425... is the root of the equation (1-r)^(2*r-1) * (1+r)^(2*r+1) = r^(4*r).
MATHEMATICA
Table[Sum[(Binomial[n+k, k]*Binomial[n, k])^k, {k, 0, n}], {n, 0, 12}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 10 2021
STATUS
approved