a(n) = 1 + Sum_{k=0..n-1} binomial(n+2,k+3) * a(k).

Terms

a(0) =1a(1) =2a(2) =7a(3) =28a(4) =121a(5) =570a(6) =2911a(7) =15968a(8) =93433a(9) =580162a(10) =3806275a(11) =26284368a(12) =190415809a(13) =1442982350a(14) =11409436363a(15) =93913277608a(16) =803094241309