A367331 a(n) = 27^n * Sum_{k=0..n} (-1)^k*binomial(1/3, k)^2.

1, 24, 657, 17664, 477828, 12888288, 348197220, 9397548288, 253804616001, 6851337236952, 185014241769825, 4994797849546752, 134872057740184128, 3641273395825798656, 98320397048549301312, 2654515896013953110016, 71674988018612154171876

Offset: 0

Author

Vaclav Kotesovec, Nov 14 2023

Keywords

• nonn

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))).

Crossrefs

Cf. A358363, A367330, A367332, A367333.

Programs

Mathematica

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

Formula

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