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) ~ 2^(5/3) * Pi * 3^(3*n + 1/2) / Gamma(1/3)^3.
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