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

0,2

Comments

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

Links

Table of n, a(n) for n=0..16.

Formula

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

Mathematica

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

Crossrefs

Cf. A358364, A367330, A367331, A367333.

Sequence in context: A261030 A160269 A367275 * A049394 A143169 A256324

Adjacent sequences: A367329 A367330 A367331 * A367333 A367334 A367335

Keyword

nonn

Author

Vaclav Kotesovec, Nov 14 2023

Status

approved