A203466 a(n) = A203306(n)/A000178(n) where A000178 are superfactorials.

1, 1, 10, 15180, 97199847360, 124679879327832253286400, 2359315315713931476611812172370616909824000, 69427548091550819116702789435220590352184299509517898727953530880000000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..16
• R. Chapman, A polynomial taking integer values, Mathematics Magazine, 29 (1996), 121.

Crossrefs

Cf. A203306.

Programs

Magma

F:= Factorial; [1] cat [(&*[(&*[F(k+1) - F(j): j in [1..k]])/Factorial(k): k in [1..n-1]]): n in [2..20]]; // G. C. Greubel, Sep 19 2023

Mathematica

f[j_]:= j!; z = 10;
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}]       (* A203306 *)
Table[v[n]/d[n], {n,z}]  (* A203466 *)

SageMath

f=factorial; [product(product(f(k+1) - f(j) for j in range(1, k+1))//factorial(k) for k in range(1, n)) for n in range(1,21)] # G. C. Greubel, Sep 19 2023

Extensions

Name edited by Michel Marcus, May 17 2019