A367330 a(n) = 27^n * Sum_{k=0..n} (-1)^k*binomial(-1/3, k)^2.

1, 24, 684, 17880, 493785, 13108608, 358702272, 9579537792, 261039317220, 6992695897440, 190104989730480, 5101807912472160, 138496042650288420, 3721234160086727040, 100918032317551270080, 2713823288825315967360, 73545091414048811297745

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))).

Links

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

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

Cf. A358362, A367331, A367332, A367333.

Sequence in context: A291066 A160038 A322746 * A184274 A093456 A189412

Adjacent sequences: A367327 A367328 A367329 * A367331 A367332 A367333

Keyword

nonn

Author

Vaclav Kotesovec, Nov 14 2023

Status

approved