OFFSET
0,3
FORMULA
a(n) ~ (4 + 3^(4/3) + 3^(5/3))^(n + 5/3) / (3^(11/6) * Pi * n^4).
a(0) = 1, a(n) = 3^n*Sum_{k=1..n} (1/3)^k*binomial(n + 1, k - 1)*binomial(n + 1, k)*binomial(n + 1, k + 1)/(binomial(n + 1, 1)*binomial(n + 1, 2)). - Detlef Meya, May 28 2024
MATHEMATICA
Table[HypergeometricPFQ[{-1-n, -n, 1-n}, {2, 3}, -3], {n, 0, 30}]
a[0] := 1; a[n_] := 3^n*Sum[(1/3)^k*Binomial[n + 1, k - 1]*Binomial[n + 1, k]*Binomial[n + 1, k + 1]/(Binomial[n + 1, 1]*Binomial[n + 1, 2]), {k, 1, n}]; Table[a[n], {n, 0, 22}] (* Detlef Meya, May 28 2024 *)
PROG
(Python)
from sympy import hyperexpand
from sympy.functions import hyper
def A368733(n): return hyperexpand(hyper((-1-n, -n, 1-n), (2, 3), -3)) # Chai Wah Wu, Jan 04 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jan 04 2024
STATUS
approved