Generalized central binomial coefficients for k=2.

Terms

a(0) =1a(1) =1a(2) =5a(3) =9a(4) =45a(5) =97a(6) =485a(7) =1145a(8) =5725a(9) =14289a(10) =71445a(11) =185193a(12) =925965a(13) =2467137a(14) =12335685a(15) =33563481a(16) =167817405a(17) =464221105a(18) =2321105525a(19) =6507351113a(20) =32536755565a(21) =92236247841a(22) =461181239205