a(n)=(1/2)*sum(i=0,n,rad(binomial(n,i))) where rad(k)=A007947(k).

Terms

a(0) =1a(1) =2a(2) =4a(3) =6a(4) =16a(5) =27a(6) =64a(7) =66a(8) =94a(9) =287a(10) =1024a(11) =645a(12) =2380a(13) =6723a(14) =12094a(15) =7136a(16) =36772a(17) =38733a(18) =161254a(19) =241083a(20) =571714a(21) =1203173a(22) =4194304a(23) =2005009a(24) =2162496a(25) =8739877a(26) =6699838a(27) =27330423a(28) =112844656a(29) =41322885