A203479 a(n) = Product_{1 <= i < j <= n} (2^i + 2^j - 2).

1, 4, 320, 2027520, 3855986196480, 8359491805553413324800, 79457890145647634305213865656320000, 12897878211365028383150895090566532213003150950400000, 140613650417826346093374124598539442743630963394643403845144815232614400000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn

Comments

Each term divides its successor, as in A203480.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..21

Crossrefs

Cf. A000225, A093883, A203305, A203480, A203481.

Programs

Magma

[(&*[(&*[2^j+2^k-2: k in [1..j]])/(2^(j+1)-2): j in [1..n]]): n in [1..15]]; // G. C. Greubel, Aug 28 2023

Maple

a:= n-> mul(mul(2^i+2^j-2, i=1..j-1), j=2..n):
seq(a(n), n=1..12);  # Alois P. Heinz, Jul 23 2017

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^j +2^k -2, {j,n}, {k,j-1}], {n,15}] (* G. C. Greubel, Aug 28 2023 *)

SageMath

[product(product(2^j+2^k-2 for k in range(1,j)) for j in range(1,n+1)) for n in range(1,16)] # G. C. Greubel, Aug 28 2023

Formula

a(n) ~ c * 2^((n-1)*n*(n+1)/3) / QPochhammer(1/2, 1/4)^(n-1), where c = 0.0732262905669624786298393270254722268761908164083517721484477901776137... - Vaclav Kotesovec, Aug 09 2025

Extensions

Name edited by Alois P. Heinz, Jul 23 2017