A203481 a(n) = v(n+1)/(4*v(n)), where v = A203479.

1, 20, 1584, 475456, 541981440, 2376277529600, 40580860464967680, 2725519037191790608384, 724680197846400799531008000, 766028090108619425976217272320000, 3227487808644444231639810280103215104000

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. A203479, A203480, A093883.

Cf. A079555.

Programs

Magma

[(&*[2^j + 2^(n+1) - 2: j in [1..n]])/4: 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}]/4, {n,20}] (* G. C. Greubel, Aug 28 2023 *)

SageMath

[product(2^j+2^(n+1)-2 for j in range(1,n+1))/4 for n in range(1,21)] # G. C. Greubel, Aug 28 2023

Formula

a(n) = (1/4)*Product_{k=1..n} (2^k + 2^(n+1) - 2). - G. C. Greubel, Aug 28 2023

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