A186271 a(n)=Product{k=0..n, A001333(k)}.

1, 1, 3, 21, 357, 14637, 1449063, 346326057, 199830134889, 278363377900377, 936136039878967851, 7600488507777339982269, 148977175240943640992454669, 7049748909576694035403947391749, 805384464676770256686653161875581007

Offset: 0

Author

Paul Barry, Feb 16 2011

Keywords

• nonn
• easy

Comments

a(n) is the determinant of the symmetric matrix (if(j<=floor((i+j)/2), Pell(j+1),

Pell(i+1)))_{0<=i,j<=n}, where Pell(n)=A000129(n).

Examples

			a(3)=21 since det[1, 1, 1, 1; 1, 2, 2, 2; 1, 2, 5, 5; 1, 2, 5, 12]=21.
		

Crossrefs

Cf. A186269.

Programs

Mathematica

Table[Product[Sum[Binomial[k,2*j]*2^j,{j,0,Floor[k/2]}],{k,0,n}],{n,0,15}] (* Vaclav Kotesovec, Jul 11 2015 *)
Table[FullSimplify[Product[((1+Sqrt[2])^k + (1-Sqrt[2])^k)/2, {k, 0, n}]], {n, 0, 15}] (* Vaclav Kotesovec, Jul 11 2015 *)

Formula

a(n)=Product{k=0..n, sum{j=0..floor(k/2), binomial(k,2j)*2^j}}.

a(n) ~ c * (1+sqrt(2))^(n*(n+1)/2) / 2^(n+1), where c = 1.6982679851338713863950411843311686297311132648098280324748781109134... . - Vaclav Kotesovec, Jul 11 2015