A203480 a(n) = v(n+1)/v(n), where v = A203479.

4, 80, 6336, 1901824, 2167925760, 9505110118400, 162323441859870720, 10902076148767162433536, 2898720791385603198124032000, 3064112360434477703904869089280000, 12909951234577776926559241120412860416000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn

Links

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

Crossrefs

Cf. A093883, A203307, A203479.

Cf. A079555.

Programs

Magma

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

Mathematica

(* First program *)
f[j_]:= 2^j - 1; z = 15;
v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]
Table[v[n], {n,z}]               (* A203479 *)
Table[v[n+1]/v[n], {n,z-1}]      (* A203480 *)
Table[v[n+1]/(4*v[n]), {n,z-1}]  (* A203481 *)
(* Second program *)
Table[Product[2^(n+1) +2^k -2, {k,n}], {n,20}] (* G. C. Greubel, Aug 28 2023 *)

SageMath

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

Formula

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

a(n) ~ c * 2^(n*(n+1)), where c = 1/QPochhammer(1/2, 1/4) = A079555 = 2.3842310290313717... - Vaclav Kotesovec, Aug 09 2025