A203432 a(n) = A203430(n)/A000178(n) where A000178=(superfactorials).

1, 2, 3, 15, 45, 540, 3402, 96228, 1299078, 85739148, 2507870079, 383704122087, 24487299427734, 8645900336407620, 1209640056157393380, 982320774834892454820, 302358334494179897593596, 563293577162657149216869348

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..100

R. Chapman, A polynomial taking integer values, Mathematics Magazine, 29 (1996), 121.

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}]             (* A203430 *)
Table[v[n+1]/v[n], {n, z}]      (* A203431 *)
Table[v[n]/d[n], {n, z}]        (* this sequence *)

Prog

(Magma)
Barnes:= func< n | (&*[Factorial(j): j in [1..n-1]]) >;
A203432:= 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]])/Barnes(n) >;
[A203432(n): n in [1..25]]; // G. C. Greubel, Sep 20 2023
(SageMath)
def barnes(n): return product(factorial(j) for j in range(n))
def A203432(n): return product(product(k-j+((k+1)//2)-((j+1)//2) for j in range(k)) for k in range(1, n))/barnes(n)
[A203432(n) for n in range(1, 31)] # G. C. Greubel, Sep 20 2023

Crossrefs

Cf. A000178, A032766, A203430, A203431.

Sequence in context: A221860 A216339 A048076 * A298409 A151369 A143885

Adjacent sequences: A203429 A203430 A203431 * A203433 A203434 A203435

Keyword

nonn

Author

Clark Kimberling, Jan 02 2012

Status

approved