STATUS
reviewed
approved
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Revision History for A203424
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
STATUS
proposed
reviewed
STATUS
editing
proposed
FORMULA
a(n) = (-2)^binomial(n,2) * (n!)^n / BarnesG(n+2). - G. C. Greubel, Dec 07 2023
MATHEMATICA
(* First program *)
1/Table[v[n], {n, 1, z}] (* A203424 *)
Table[v[n]/(4 v[n + 1]), {n, 1, z - 1}] (* A203425 *)
(* Second program *)
Table[(-2)^Binomial[n, 2]*(n!)^n/BarnesG[n+2], {n, 20}] (* G. C. Greubel, Dec 07 2023 *)
PROG
(Magma)
BarnesG:= func< n | (&*[Factorial(k): k in [0..n-2]]) >;
A203424:= func< n| (-2)^Binomial(n, 2)*(Factorial(n))^n/BarnesG(n+2) >;
[A203424(n): n in [1..20]]; // G. C. Greubel, Dec 07 2023
(SageMath)
def BarnesG(n): return product(factorial(k) for k in range(n-1))
def A203424(n): return (-2)^binomial(n, 2)*(gamma(n+1))^n/BarnesG(n+2)
[A203424(n) for n in range(1, 21)] # G. C. Greubel, Dec 07 2023
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
FORMULA
a(n) = 2^binomial(n,2) * A203421(n). - Kevin Ryde, May 03 2022
PROG
(PARI) a(n) = prod(k=2, n, (-k)^(k-1)) << binomial(n, 2); \\ Kevin Ryde, May 03 2022
KEYWORD
sign,easy
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed