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

Terms

a(0) =1a(1) =6a(2) =19a(3) =88a(4) =337a(5) =1242a(6) =4623a(7) =16652a(8) =59389a(9) =209902a(10) =734491a(11) =2553024a(12) =8819753a(13) =30306498a(14) =103669991a(15) =353201460a(16) =1199086357a(17) =4057965398a(18) =13694169715a(19) =46095091816a(20) =154799435457a(21) =518763845034