G.f.: 1/AGM(1, (1-4*x)^2).

Terms

a(0) =1a(1) =4a(2) =12a(3) =32a(4) =84a(5) =240a(6) =784a(7) =2816a(8) =10404a(9) =38096a(10) =137456a(11) =493440a(12) =1783376a(13) =6532288a(14) =24245568a(15) =90814464a(16) =341776164a(17) =1289126160a(18) =4870386736a(19) =18439692928a(20) =70004793936a(21) =266551445952