a(n) = Sum_{k=0..floor((n-3)/5)} Stirling2(n,5*k+3).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =6a(5) =25a(6) =90a(7) =301a(8) =967a(9) =3061a(10) =10080a(11) =40381a(12) =245553a(13) =2161238a(14) =21701381a(15) =219007491a(16) =2149071359a(17) =20442363031a(18) =189226358659