a(n) = binomial(2*n,n) * Fibonacci(n)/2.

Terms

a(0) =0a(1) =1a(2) =3a(3) =20a(4) =105a(5) =630a(6) =3696a(7) =22308a(8) =135135a(9) =826540a(10) =5080790a(11) =31391724a(12) =194699232a(13) =1211669900a(14) =7561979100a(15) =47310843600a(16) =296633172465