a(n) = n! * Sum_{i+2j+3k=n} 1/(i!*(2j)!*(3k)!).

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =12a(5) =36a(6) =113a(7) =351a(8) =1080a(9) =3281a(10) =9882a(11) =29646a(12) =88817a(13) =266085a(14) =797526a(15) =2391485a(16) =7173360a(17) =21520080a(18) =64563521a(19) =193700403a(20) =581120892a(21) =1743392201a(22) =5230206126a(23) =15690618378a(24) =47071766561a(25) =141215033961a(26) =423644570442