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

Terms

a(0) =1a(1) =2a(2) =15a(3) =64a(4) =233a(5) =926a(6) =3411a(7) =12380a(8) =44605a(9) =158074a(10) =555687a(11) =1938488a(12) =6715217a(13) =23135190a(14) =79313403a(15) =270741396a(16) =920731749a(17) =3120733874a(18) =10545871951a(19) =35542007920a(20) =119494151033a(21) =400860857358