A203433 Vandermonde determinant of the first n terms of (2,3,5,6,8,9,...) = (j+floor((j+1)/2)).

1, 1, 6, 72, 12960, 6531840, 84652646400, 3839844040704000, 6568897997313146880000, 46482573252667397426380800000, 16698920220108665726304214056960000000, 28359415513133792655802758561911537664000000000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn

Comments

Each term divides its successor, as in A014402, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203434.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..41

Crossrefs

Cf. A000178, A007494, A014402, A203434.

Programs

Magma

A203433:= func< n | n eq 1 select 1 else (&*[(&*[k-j+Floor(k/2)-Floor(j/2): j in [0..k-1]]) : k in [1..n-1]]) >;
[A203433(n): n in [1..25]]; // G. C. Greubel, Sep 20 2023

Mathematica

f[j_]:= j + Floor[(j+1)/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}]             (* this sequence *)
Table[v[n+1]/v[n], {n,z}]      (* A014402 *)
Table[v[n]/d[n], {n,z}]        (* A203434 *)

SageMath

def A203433(n): return product(product(k-j+(k//2)-(j//2) for j in range(k)) for k in range(1,n))
[A203433(n) for n in range(1,31)] # G. C. Greubel, Sep 20 2023