A203307 a(n) = v(n+1)/(2*v(n)), where v = A203305.

1, 12, 672, 161280, 159989760, 645078712320, 10486399547473920, 684552162459097497600, 179100751368498596492083200, 187617350297573441752474740326400, 786539962489104046627462744981792358400

Offset: 1

Author

Clark Kimberling, Jan 01 2012

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A203305, A028365.

Programs

Magma

[(&*[2^(n+1) - 2^(j+1): j in [0..n-1]])/2: n in [1..20]]; // G. C. Greubel, Aug 31 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}]         (* A203305 *)
Table[v[n+1]/v[n], {n,z}]  (* A028365 *)
%/2                         (* A203307 *)
(* Second program *)
Table[(-1)^n*2^Binomial[n+1,2]*QPochhammer[2,2,n]/2, {n,20}] (* G. C. Greubel, Aug 31 2023 *)

SageMath

[product(2^(n+1) - 2^(k+1) for k in range(n))/2 for n in range(1,21)] # G. C. Greubel, Aug 31 2023

Formula

a(n) = (1/2)*A028365(n) for n>0.

a(n) = (-1)^n * 2^(binomial(n+1,2) - 1) * QPochhammer(2,2,n). - G. C. Greubel, Aug 31 2023