Sum {binomial(n,k)^2*J(k+1),k,0,n} with J(n)=A001045(n).

Terms

a(0) =1a(1) =2a(2) =8a(3) =42a(4) =216a(5) =1122a(6) =5986a(7) =32426a(8) =177176a(9) =975042a(10) =5398218a(11) =30031146a(12) =167730954a(13) =939955746a(14) =5282564358a(15) =29761587882a(16) =168036828696a(17) =950556482946