a(0) = 1, a(1) = 2; for k>0, a(2*k) = k*a(2*k-1) + a(2*k-2), a(2*k+1) = a(2*k) + a(2*k-1).

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =13a(5) =18a(6) =67a(7) =85a(8) =407a(9) =492a(10) =2867a(11) =3359a(12) =23021a(13) =26380a(14) =207681a(15) =234061a(16) =2080169a(17) =2314230a(18) =22908239a(19) =25222469a(20) =275132929a(21) =300355398a(22) =3579042307a(23) =3879397705a(24) =50131814767a(25) =54011212472a(26) =752277576903a(27) =806288789375