A203430 Vandermonde determinant of the first n numbers (1,3,4,6,7,9,10,...) = (j+floor(j/2)).

1, 2, 6, 180, 12960, 18662400, 84652646400, 12068081270784000, 6568897997313146880000, 157325632547489652827750400000, 16698920220108665726304214056960000000, 101984821172231138973752227905335721984000000000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn

Comments

Each term divides its successor, as in A203431, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203432.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..40

Crossrefs

Cf. A032766, A203431, A203432.

Programs

Magma

A203430:= func< n | n eq 1 select 1 else (&*[(&*[k-j+Floor((k+1)/2)-Floor((j+1)/2): j in [0..k-1]]) : k in [1..n-1]]) >;
[A203430(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}]            (* this sequence *)
Table[v[n+1]/v[n], {n,z}]     (* A203431 *)
Table[v[n]/d[n], {n,z}]       (* A203432 *)

SageMath

def A203430(n): return product(product(k-j+((k+1)//2)-((j+1)//2) for j in range(k)) for k in range(1, n))
[A203430(n) for n in range(1, 31)] # G. C. Greubel, Sep 27 2023