a(n) = Sum_{k=0..floor((n-4)/5)} Stirling2(n,5*k+4).

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =1a(5) =10a(6) =65a(7) =350a(8) =1701a(9) =7771a(10) =34150a(11) =146905a(12) =633776a(13) =2892032a(14) =15526876a(15) =109484545a(16) =992589171a(17) =10223409493a(18) =108982611518