From a differential equation.

Terms

a(0) =0a(1) =1a(2) =0a(3) =0a(4) =1a(5) =2a(6) =3a(7) =5a(8) =12a(9) =36a(10) =110a(11) =326a(12) =963a(13) =2964a(14) =9797a(15) =34818a(16) =130585a(17) =506996a(18) =2018454a(19) =8238737a(20) =34627390a(21) =150485325a(22) =677033911a(23) =3147372610a(24) =15066340824a(25) =74025698886a(26) =372557932434