Array of ((k^n)+(k^(-n)))/2 where k=(sqrt(x^2+1)+x)^2 for integers x>=1.

Terms

a(0) =1a(1) =3a(2) =1a(3) =17a(4) =9a(5) =1a(6) =99a(7) =161a(8) =19a(9) =1a(10) =577a(11) =2889a(12) =721a(13) =33a(14) =1a(15) =3363a(16) =51841a(17) =27379a(18) =2177a(19) =51a(20) =1a(21) =19601a(22) =930249a(23) =1039681a(24) =143649a(25) =5201a(26) =73a(27) =1a(28) =114243a(29) =16692641