G.f.: (1/2)*(3 - sqrt((1-5*x)/(1-x))).

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =15a(5) =51a(6) =188a(7) =731a(8) =2950a(9) =12235a(10) =51822a(11) =223191a(12) =974427a(13) =4302645a(14) =19181100a(15) =86211885a(16) =390248055a(17) =1777495635a(18) =8140539950a(19) =37463689775a(20) =173164232965a(21) =803539474345