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

1,2

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A032766, A203431, A203432.

Sequence in context: A182523 A137532 A072116 * A298883 A252740 A055696

Adjacent sequences: A203427 A203428 A203429 * A203431 A203432 A203433

Keyword

nonn

Author

Clark Kimberling, Jan 02 2012

Status

approved