G.f.: Sum_{n>=0} x^n * ( (1+x)^n + (1-x)^n )^n / 2^n.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =3a(5) =10a(6) =26a(7) =78a(8) =311a(9) =1200a(10) =4626a(11) =20831a(12) =98953a(13) =468700a(14) =2399950a(15) =13084381a(16) =72319603a(17) =418017254a(18) =2545312690a(19) =15862538760a(20) =102062357538a(21) =684056780835