a(n) = floor(Sum_{m=1..n} Stirling2(n,m) / binomial(n-1,m-1)).

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =12a(5) =26a(6) =62a(7) =161a(8) =448a(9) =1338a(10) =4274a(11) =14524a(12) =52289a(13) =198678a(14) =794065a(15) =3328482a(16) =14594217a(17) =66779091a(18) =318205958a(19) =1575994324a(20) =8098891289a(21) =43115440260a(22) =237435483669