A203684 v(n+1)/v(n), where v=A203683.

5, 340, 353600, 5816012800, 1526121758720000, 6402581345767260160000, 429696185755224300427673600000, 461389806400964771465272438344908800000, 7926646754442012918793099237780758028353536000000

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..40

Programs

Maple

f:= n -> ((5*4^(n*(n+1)))/(4^(n+1)+1))*mul(1+4^(k-(n+1)),k=0..n-1);
seq(f(n), n=1..20); # Robert Israel, Dec 15 2014

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]:=(5 4^(n (n+1)))/(4^(n+1)+1) QPochhammer[-4^-(n+1),4,n] (* Todd Silvestri, Nov 16 2014 *)

Formula

a(n) = ((5*4^(n*(n+1)))/(4^(n+1)+1))*(-4^-(n+1);4)n, where the q-Pochhammer symbol (c;q)_m = product(1-c*q^j, j = 0..m-1). - _Todd Silvestri, Nov 16 2014

a(n+1) = (4^n + 4^(2*n+1))*a(n). - Robert Israel, Dec 15 2014