a(n) = 5^n*Sum_{ k=0..n } binomial(2*k,k)/5^k.

Terms

a(0) =1a(1) =7a(2) =41a(3) =225a(4) =1195a(5) =6227a(6) =32059a(7) =163727a(8) =831505a(9) =4206145a(10) =21215481a(11) =106782837a(12) =536618341a(13) =2693492305a(14) =13507578125a(15) =67693008145a(16) =339066121115