Sum(sum(binomial(i,j),i=n..2*n),j=0..n).

Terms

a(0) =1a(1) =5a(2) =22a(3) =91a(4) =366a(5) =1454a(6) =5748a(7) =22691a(8) =89590a(9) =354010a(10) =1400268a(11) =5544334a(12) =21973420a(13) =87158972a(14) =345977832a(15) =1374249251a(16) =5461704870a(17) =21717305762a(18) =86391846492a(19) =343800647066