G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k)^2 * x^k*(2-x)^(n-k).

Terms

a(0) =1a(1) =2a(2) =4a(3) =12a(4) =38a(5) =116a(6) =360a(7) =1144a(8) =3670a(9) =11836a(10) =38392a(11) =125160a(12) =409628a(13) =1345000a(14) =4428752a(15) =14618608a(16) =48356838a(17) =160260332a(18) =532009688a(19) =1768729736a(20) =5888250996a(21) =19626282328a(22) =65489004464a(23) =218743627408a(24) =731311554044