|
| |
|
|
A203430
|
|
Vandermonde determinant of the first n numbers (1,3,4,6,7,9,10,...) = (j+floor(j/2)).
|
|
4
|
|
|
|
1, 2, 6, 180, 12960, 18662400, 84652646400, 12068081270784000, 6568897997313146880000, 157325632547489652827750400000, 16698920220108665726304214056960000000, 101984821172231138973752227905335721984000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
|
|
|
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]]) >;
(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))
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
