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

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

Offset

1,2

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.

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 *)

Prog

(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
(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

Crossrefs

Cf. A203305.

Sequence in context: A242484 A088912 A342573 * A055462 A088600 A066120

Adjacent sequences: A203462 A203463 A203464 * A203466 A203467 A203468

Keyword

nonn

Author

Clark Kimberling, Jan 02 2012

Extensions

Name edited by Michel Marcus, May 17 2019

Status

approved