A203478 a(n) = v(n+1)/v(n), where v = A203477.

3, 30, 1080, 146880, 77552640, 161309491200, 1331771159347200, 43809944057885491200, 5753472333233985788313600, 3019422280481195741706977280000, 6335279362770913356551778761441280000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..55

Crossrefs

Cf. A028362, A093883, A164051, A203307, A203477.

Programs

Magma

[(&*[2^j + 2^n: j in [0..n-1]]): n in [1..20]]; // G. C. Greubel, Aug 28 2023

Mathematica

(* First program *)
f[j_]:= 2^(j-1); z = 13;
v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]
Table[v[n], {n,z}]                       (* A203477 *)
Table[v[n+1]/v[n], {n,z-1}]              (* A203478 *)
Table[v[n]*v[n+2]/(2*v[n+1]^2), {n,22}]  (* A164051 *)
(* Second program *)
Table[Product[2^j +2^n, {j,0,n-1}], {n,20}] (* G. C. Greubel, Aug 28 2023 *)

PARI

a(n)=prod(i=0,n-1,2^i+2^n) \\ Charles R Greathouse IV, Feb 16 2021

SageMath

[product(2^j + 2^n for j in range(n)) for n in range(1,21)] # G. C. Greubel, Aug 28 2023

Formula

a(n) = A028362(n+1) * 2^(n*(n-1)/2). - Charles R Greathouse IV, Feb 16 2021

a(n) = Product_{j=0..n-1} (2^j + 2^n). - G. C. Greubel, Aug 28 2023