a(n) = Sum_{i=0..n+1} binomial(2*n,n-i+1).

Terms

a(0) =1a(1) =4a(2) =15a(3) =57a(4) =219a(5) =848a(6) =3302a(7) =12911a(8) =50643a(9) =199140a(10) =784626a(11) =3096514a(12) =12236830a(13) =48412432a(14) =191718188a(15) =759852347a(16) =3013746563a(17) =11960699132a(18) =47494802618a(19) =188689585982a(20) =749961486698