T(n+4,4) with T as in A036355.

Terms

a(0) =5a(1) =20a(2) =71a(3) =207a(4) =556a(5) =1390a(6) =3310a(7) =7576a(8) =16807a(9) =36331a(10) =76850a(11) =159575a(12) =326092a(13) =657124a(14) =1307992a(15) =2575180a(16) =5020570a(17) =9702043a(18) =18599391a(19) =35397328a(20) =66918850a(21) =125738650a(22) =234930380a(23) =436660010a(24) =807690455a(25) =1487269940a(26) =2727149885a(27) =4981046893