A203465 a(n) = A203305(n)/A000178(n) where A000178 are superfactorials.

1, 2, 24, 5376, 72253440, 192663508746240, 345230911480770991226880, 1436598918224589625071929521581588480, 48781096034575545526663437061892218092260229434572800

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..22
• R. Chapman, A polynomial taking integer values, Mathematics Magazine, 29 (1996), 121.

Crossrefs

Cf. A203305.

Programs

Magma

F:= Factorial; [1] cat [(&*[(&*[2^(k+1) - 2^(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_]:= 2^j - 1; 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}]         (* A203305 *)
Table[v[n]/d[n], {n,z}]    (* A203465 *)

SageMath

f=factorial; [product(product(2^(k+1) - 2^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