A203683 Vandermonde sequence using x^2 + y^2 applied to (1,2,4,...,2^(n-1)).

1, 5, 1700, 601120000, 3496121614336000000, 5335507266769461885009920000000000, 34161019296423817239835748940949012820787200000000000000

Offset: 1

Author

Clark Kimberling, Jan 04 2012

Keywords

• nonn

Comments

See A093883 for a discussion and guide to related sequences.

Links

• Todd Silvestri, Table of n, a(n) for n = 1..17

Programs

Mathematica

f[j_] := 2^(j - 1); z = 12;
u[n_] := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]
v[n_] := Product[u[n], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203683 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203684 *)
a[n_Integer/;n>=1]:=Product[(5 4^(k (k+1)))/(4^(k+1)+1) QPochhammer[-4^-(k+1),4,k],{k,n-1}] (* Todd Silvestri, Dec 15 2014 *)

Formula

a(n) = product(((5*4^(k*(k+1)))/(4^(k+1)+1))*(-4^-(k+1);4)k, k = 1..n-1), where the q-Pochhammer symbol (c;q)_m = product(1-c*q^j, j = 0..m-1). - _Todd Silvestri, Dec 15 2014