OFFSET
0,2
COMMENTS
In general, for m>1, Sum_{k>=0} (-1)^k * binomial(-1/m,k)^2 = 2^(-1/m) * sqrt(Pi) / (Gamma(1 - 1/(2*m)) * Gamma(1/2 + 1/(2*m))).
FORMULA
a(n) ~ Gamma(1/3)^3 * 3^(3*n+1) / (2^(8/3) * Pi^2).
MATHEMATICA
Table[27^n*Sum[(-1)^k*Binomial[-1/3, k]^2, {k, 0, n}], {n, 0, 16}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 14 2023
STATUS
approved