A203431 a(n) = v(n+1)/v(n), where v=A203430.

2, 3, 30, 72, 1440, 4536, 142560, 544320, 23950080, 106142400, 6107270400, 30569011200, 2198617344000, 12197035468800, 1061932177152000, 6440034727526400, 662645678542848000, 4347023441080320000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A032766, A203430, A203432.

Programs

Magma

A203431:= func< n | n eq 1 select 2 else (&*[n-j+Floor((n+1)/2)-Floor((j+1)/2): j in [0..n-1]]) >;
[A203431(n): n in [1..25]]; // G. C. Greubel, Sep 27 2023

Mathematica

f[j_]:= j + Floor[j/2]; z = 20;
v[n_]:= Product[Product[f[k] - f[j], {j,k-1}], {k,2,n}]
d[n_]:= Product[(i-1)!, {i,n}]
Table[v[n], {n,z}]            (* A203430 *)
Table[v[n+1]/v[n], {n,z}]     (* this sequence *)
Table[v[n]/d[n], {n,z}]       (* A203432 *)

SageMath

def A203431(n): return product(n-j+((n+1)//2)-((j+1)//2) for j in range(n))
[A203431(n) for n in range(1, 31)] # G. C. Greubel, Sep 27 2023

Extensions

Typo in the definition corrected by Vaclav Kotesovec, Jun 09 2025