Riordan array (((1+x)/(1-x-x^2))^m, x*A000108(x)), m=2.

Terms

a(0) =1a(1) =4a(2) =1a(3) =10a(4) =5a(5) =1a(6) =22a(7) =16a(8) =6a(9) =1a(10) =45a(11) =45a(12) =23a(13) =7a(14) =1a(15) =88a(16) =121a(17) =76a(18) =31a(19) =8a(20) =1a(21) =167a(22) =325a(23) =237a(24) =116a(25) =40a(26) =9a(27) =1a(28) =310a(29) =895