|
%I #18 Dec 17 2014 21:13:03
%S 5,340,353600,5816012800,1526121758720000,6402581345767260160000,
%T 429696185755224300427673600000,
%U 461389806400964771465272438344908800000,7926646754442012918793099237780758028353536000000
%N v(n+1)/v(n), where v=A203683.
%C See A093883 for a discussion and guide to related sequences.
%H Todd Silvestri, <a href="/A203684/b203684.txt">Table of n, a(n) for n = 1..40</a>
%F 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
%F a(n+1) = (4^n + 4^(2*n+1))*a(n). - _Robert Israel_, Dec 15 2014
%p f:= n -> ((5*4^(n*(n+1)))/(4^(n+1)+1))*mul(1+4^(k-(n+1)),k=0..n-1);
%p seq(f(n), n=1..20); # _Robert Israel_, Dec 15 2014
%t f[j_] := 2^(j - 1); z = 12;
%t u[n_] := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]
%t v[n_] := Product[u[n], {k, 2, n}]
%t Table[v[n], {n, 1, z}] (* A203683 *)
%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203684 *)
%t 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 *)
%K nonn
%O 1,1
%A _Clark Kimberling_, Jan 04 2012
| 