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

1,3

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A000178, A007494, A014402, A203434.

Sequence in context: A166472 A182917 A328814 * A008562 A367350 A041063

Adjacent sequences: A203430 A203431 A203432 * A203434 A203435 A203436

Keyword

nonn

Author

Clark Kimberling, Jan 02 2012

Status

approved