%I #8 Nov 14 2023 17:27:15

%S 1,24,684,17880,493785,13108608,358702272,9579537792,261039317220,

%T 6992695897440,190104989730480,5101807912472160,138496042650288420,

%U 3721234160086727040,100918032317551270080,2713823288825315967360,73545091414048811297745

%N a(n) = 27^n * Sum_{k=0..n} (-1)^k*binomial(-1/3, k)^2.

%C 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))).

%F a(n) ~ Gamma(1/3)^3 * 3^(3*n+1) / (2^(8/3) * Pi^2).

%t Table[27^n*Sum[(-1)^k*Binomial[-1/3, k]^2, {k, 0, n}], {n, 0, 16}]

%Y Cf. A358362, A367331, A367332, A367333.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Nov 14 2023