A367332 a(n) = 27^n * Sum_{k=0..n} binomial(1/3, k)^2.

1, 30, 819, 22188, 599976, 16212420, 437948784, 11828393820, 319437445365, 8626198419930, 232935493710231, 6289845008414760, 169838331029620344, 4585907100958922088, 123825507087143633976, 3343423515649756142760, 90275493748778836055964

Offset: 0

Author

Vaclav Kotesovec, Nov 14 2023

Keywords

• nonn

Comments

In general, for m>1, Sum_{k>=0} binomial(1/m,k)^2 = Gamma(1 + 2/m) / Gamma(1 + 1/m)^2.

Crossrefs

Cf. A358364, A367330, A367331, A367333.

Programs

Mathematica

Table[27^n*Sum[Binomial[1/3, k]^2, {k, 0, n}], {n, 0, 16}]

Formula

a(n) ~ 4 * Pi * 3^(3*n + 1/2) / Gamma(1/3)^3.