OFFSET
1,2
COMMENTS
Each term divides its successor, as in A203429.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..33
FORMULA
a(n) = (-3)^binomial(n,2) * (Gamma(n+1))^(n-1) / BarnesG(n+1). - G. C. Greubel, Sep 28 2023
MATHEMATICA
(* First program *)
f[j_]:= 1/(3*j); z = 16;
v[n_]:= Product[Product[f[k] - f[j], {j, k-1}], {k, 2, n}]
1/Table[v[n], {n, z}] (* A203428 *)
Table[v[n]/(3*v[n+1]), {n, z}] (* A203429 *)
(* Second program *)
Table[(-3)^Binomial[n, 2]*(Gamma[n+1])^(n-1)/BarnesG[n+1], {n, 20}] (* G. C. Greubel, Sep 28 2023 *)
PROG
(Magma)
Barnes:= func< n | (&*[Factorial(j): j in [1..n-1]]) >;
A203428:= func< n | (-3)^Binomial(n, 2)*(Factorial(n))^n/Barnes(n+1) >;
[A203428(n): n in [1..25]]; // G. C. Greubel, Sep 28 2023
(SageMath)
def barnes(n): return product(factorial(j) for j in range(n))
def A203428(n): return (-3)^binomial(n, 2)*(factorial(n))^n/barnes(n+1)
[A203428(n) for n in range(1, 21)] # G. C. Greubel, Sep 28 2023
CROSSREFS
KEYWORD
sign
AUTHOR
Clark Kimberling, Jan 02 2012
STATUS
approved